List of Papers (Satoru Odake)

nn: English, Jnn: Japanese
OA: open access (free)

96.  Type II Multi-indexed Little q-Jacobi and Little q-Laguerre Polynomials

S. Odake
arXiv:2402.17272(v1) [math-ph] [ pdf ]
23 pages, DPSU-24-1
typo (2402.17272(v1)):
* page 1, 4th line of sec.1: the the ==> the
* page 2, 2 line above sec.2: the the ==> the

95.  Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme

S. Odake
J. Math. Anal. Appl. 540 (2024) 128591 (25pp) [ DOI:10.1016/j.jmaa.2024.128591 ]
arXiv:2301.00678(v3) [math.CA] [ pdf, v1pdf ]
31 pages, DPSU-22-3 (v1:44 pages)
typo (2301.00678(v3)):
* page 15, 1 line above (4.40): another ==> other
typo (2301.00678(v1)):
* page 41, sec.A.4, 2nd line : discrete Hermite ==> discrete q-Hermite (two places)

94.  New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations

S. Odake
Prog. Theor. Exp. Phys. 2023 (2023) 073A01 (39pp) [ DOI:10.1093/ptep/ptad077 ]
arXiv:2209.12353(v2) [math-ph] [ pdf ]
50 pages, DPSU-22-2
typo (2209.12353(v2)):
* page 18, (4.15), 3rd line, end: ), ==> ) (deleta ",")
* page 21, (4.33), 3rd line: \check{\Xi}^{Q,monic} ==> \check{\Xi}^{Q monic} (delete ",")
* page 27, A.1.2, 2nd line, end : \rho=1 ==> \rho=1, (add ",")

93.  "Diophantine" and Factorisation Properties of Finite Orthogonal Polynomials in the Askey Scheme

S. Odake and R. Sasaki
J. Differ. Equ. Appl. 30 (2024) 820-848 [ DOI:10.1080/10236198.2024.2336476 ]
arXiv:2207.14479(v1) [math.CA] [ pdf, revisedpdf ]
31 pages, DPSU-22-1

92.  Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts

S. Odake
J. Math. Phys. 64 (2023) 053503 (21pp) [ DOI:10.1063/5.0152234 ]
arXiv:2112.09358(v2) [math-ph] [ pdf, v1(typo corrected)pdf ]
32 pages, DPSU-21-2 (v1:50 pages)
typo (2112.09358(v2)):
* page 4, 1st line above (2.1) : P_n(y)'s ==> P_n(\eta)'s
* page 8, 4th line : following sections ==> next section
* page 11, 6th line from bottom : d^{II}_{s_{II}} ==> d^{II}_{M_{II}}
* page 14, Remark 3.1, 2nd line : are ==> is
* page 32, [26], 2nd line : arXiv:arXiv ==> arXiv

91.  Markov Chains Generated by Convolutions of Orthogonality Measures

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 55 (2022) 275201 (42pp) [ DOI:10.1088/1751-8121/ac736a ]
 ((4.76), next eq. of (4.79), (5.6), (5.31) : typos by publisher)
arXiv:2106.04082(v3) [math.PR] [ pdf ]
46 pages, DPSU-21-1

90.  Free Oscillator Realization of the Laguerre Polynomial

S. Odake
Theoret. and Math. Phys. 210 (2022) 1-7 [ DOI:10.4213/tmf10120 ] [ English version DOI:10.1134/S0040577922010019 ]
arXiv:2008.10756(v2) [math-ph] [ pdf ]
8 pages, DPSU-20-2

89.  Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems

S. Odake
J. Phys. A: Math. Theor. 53 (2020) 365202 (21pp) [ DOI:10.1088/1751-8121/aba0ef ]
arXiv:2003.00219(v2) [math-ph] [ pdf ]
25 pages, DPSU-20-1

88.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types

S. Odake
J. Math. Phys. 61 (2020) 053505 (25pp) [ DOI:10.1063/1.5144338 ]
arXiv:1912.12381(v1) [math-ph] [ pdf ]
40 pages, DPSU-19-2

87.  Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types

S. Odake
Prog. Theor. Exp. Phys. 2019 (2019) 123A01 (20pp) [ DOI:10.1093/ptep/ptz124 ]
arXiv:1907.12218(v2) [math-ph] [ pdf ]
27 pages, DPSU-19-1
typo (1907.12218(v2)):
* page 1, abstract, line 5 : are ==> is
* page 1, section 1, line 4 : harmonica ==> harmonic
* page 3, line 7 from bottom : system is ==> system are
* page 8, eq.(3.6), 1 line : type II ==> type II : (add a colon)
* page 17, eq.(4.12), LHS of 2nd eq. : r^{I}_j ==> r_j (delete a superscript I)

86.  Dual Polynomials of the Multi-Indexed (q-)Racah Orthogonal Polynomials

S. Odake
Prog. Theor. Exp. Phys. 2018 (2018) 073A02 (23pp) [ DOI:10.1093/ptep/pty076 ]
arXiv:1805.00345(v2) [math-ph] [ pdf ]
31 pages, DPSU-18-2
typo (1805.00345(v2)):
* page 22, line 11 : difference equations ==> differential or difference equations
* page 27, ref.[3] : 705718 ==> 705-718
* page 31, ref.[48] : 1606.0283 ==> 1606.02836

85.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and q-Racah types

S. Odake
J. Math. Phys. 60 (2019) 023508 (30pp) [ DOI:10.1063/1.5038057 ]
arXiv:1804.10352(v2) [math-ph] [ pdf ]
45 pages, DPSU-18-1

84.  Casoratian Identities for the Discrete Orthogonal Polynomials in Discrete Quantum Mechanics with Real Shifts

S. Odake
Prog. Theor. Exp. Phys. 2017(12) (2017) 123A02 (30pp) [ DOI:10.1093/ptep/ptx165 ]
arXiv:1708.01830(v2) [math-ph] [ pdf ]
37 pages, DPSU-17-2
typo (1708.01830(v2)):
* page 13, eq.(3.42) : (qd^{-\frac12})^{\text{v}} ==> (qd^{-\frac12})^{-\text{v}}
* page 14, 1 line above (3.45) : is ==> are

83.  New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics

S. Odake
Prog. Theor. Exp. Phys. 2017(5) (2017) 053A01 (36pp) [ DOI:10.1093/ptep/ptx051 ]
arXiv:1702.03078(v2) [math-ph] [ pdf ]
43 pages, DPSU-17-1
typo (1702.03078(v2)):
* page 12, eq.(2.64) : W ==> W_C

82.  Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials

S. Odake and R. Sasaki
SIGMA 13 (2017) 020 (10pp) [ DOI:10.3842/SIGMA.2017.020 ]
arXiv:1612.00927(v3) [math.CA] (v3:SIGMA version, v2:our style) [ pdf, pdf(v2) ]
10 pages (14 pages: v2), DPSU-16-4

81.  Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 50 (2017) 165204 (23pp) [ DOI:10.1088/1751-8121/aa6496 ]
arXiv:1610.09854(v2) [math.CA] [ pdf ]
29 pages, DPSU-16-3

80.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators,

S. Odake
J. Math. Phys. 57 (2016) 113503 (22pp) [ DOI:10.1063/1.4966985 ]
arXiv:1606.02836(v1) [math-ph] [ pdf ]
33 pages, DPSU-16-2
typo (1606.02836(v1)):
* page 9, eq.(3.21) 2nd line : p_{Kj})) ==> p_{Kj})

79.  Orthogonal Polynomials from Hermitian Matrices II

S. Odake and R. Sasaki
J. Math. Phys. 59 (2018) 013504 (42pp) [ DOI:10.1063/1.5021462 ]
arXiv:1604.00714(v2) [math.CA] [ pdf ]
65 pages, DPSU-16-1

J17.  解ける量子力学模型と直交多項式

小竹 悟
日本物理学会誌 第71巻第3号 (2016年3月) 156-163 (解説) [ DOI:10.11316/butsuri.71.3_156 ] OA
タイポ :
* 図1 : (left,bottom) \phi_1 ==> \phi_0

Exactly Solvable Quantum Mechanics and Orthogonal Polynomials

S. Odake
Butsuri(The Physical Society of Japan) Vol.71, No.3 (2016) 156-163 [ DOI:10.11316/butsuri.71.3_156 ] OA
typo :
* fig.1 : (left,bottom) \phi_1 ==> \phi_0

78.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III

S. Odake
J. Math. Phys. 57 (2016) 023514 (24pp) [ DOI:10.1063/1.4941087 ]
arXiv:1509.08213(v2) [math-ph] [ pdf ]
37 pages, DPSU-15-1
typo (1509.08213(v2)):
* page 2, 3 lines above eq.(1.1) : multi-index ==> multi-indexed
* page 6, eq.(2.13) : \mathbb{Z}_{n\geq 0} ==> \mathbb{Z_{\geq 0}
* page 9, eq.(3.3) : a^{i,j}_r ==> a^{ij}_r (two places)
* page 13, eq.(3.24), 2nd equation : \Gamma_j ==> \Gamma
* page 29, eq.(B.2), \mathcal{H} in the 1st line : sin x^2 ==> sin^2 x, cos x^2 ==> cos^2 x

77.  Reflectionless Potentials for Difference Schr\"odinger Equations

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 48 (2015) 115204 (21pp) [ DOI:10.1088/1751-8113/48/11/115204 ]
arXiv:1411.2307(v2) [math-ph] [ pdf ]
24 pages, DPSU-14-2
Comment: Eq.(3.54) should be modified and/or some condition should be imposed.

76.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II

S. Odake
J. Math. Phys. 56 (2015) 053506 (18pp) [ DOI:10.1063/1.4921230 ]
arXiv:1410.8236(v2) [math-ph] [ pdf, data ]
27 pages, DPSU-14-3
typo (1410.8236(v2)):
* page 6, eq.(2.13) : \delta_{m n+k}, ==> \delta_{m,n+k}
* page 7, 1 line above eq.(3.1) : g(z) ==> g(x)
* page 9, 2nd line : Remark 5 ==> Remark 6
* page 9, Remark 4, 3rd line : Y(\eta)=2\Xi_{\ell}(\eta) ==> Y(\eta)=2\partial_{\eta}\Xi_{\ell}(\eta)
* page 11, 2nd line from bottom : g(z) ==> g(x)
* page 23, eq.(B.12) first line, denominator in r.h.s : (1+q)\sigma_1 ==> (1+q)\sigma_2
* page 23, eq.(B.12) last line : A, ==> A.

75.  Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm

S. Odake and R. Sasaki
J. Math. Phys. 56 (2015) 073502 (25pp) [ DOI:10.1063/1.4926351 ]
arXiv:1406.2768(v2) [math-ph] [ pdf ]
37 pages, DPSU-14-1

74.  Equivalences of the Multi-Indexed Orthogonal Polynomials

S. Odake
J. Math. Phys. 55 (2014) 013502 (17pp) [ DOI:10.1063/1.4859795 ]
arXiv:1309.2346(v2) [math-ph] [ pdf ]
25 pages, DPSU-13-4
typo (1309.2346(v2)):
* page 20, eq.(A.39) : P_{\mathcal{D}} ==> P_{\mathcal{D},n}
* page 21, 1 line above eq.(A.42) : c^{I}_n, c^{II}_n ==> c^{I}_{\text{v}}, c^{II}_{\text{v}}

73.  Casoratian Identities for the Wilson and Askey-Wilson Polynomials

S. Odake and R. Sasaki
J. Approx. Theory 193 (2015) 184-209 [ DOI:10.1016/j.jat.2014.04.009 ]
arXiv:1308.4240(v2) [math-ph] [ pdf ]
31 pages, 2 figures, DPSU-13-2

72.  Non-polynomial extensions of solvable potentials a la Abraham-Moses

S. Odake and R. Sasaki
J. Math. Phys. 54 (2013) 102106 (19pp) [ DOI:10.1063/1.4826475 ]
arXiv:1307.0910(v1) [math-ph] [ pdf ]
29 pages, DPSU-13-3
typo (1307.0910(v1)):
* page 13, eq.(2.56) : \varphi_1 ==> \phi_d (2 places)

71.  Recurrence Relations of the Multi-Indexed Orthogonal Polynomials

S. Odake
J. Math. Phys. 54 (2013) 083506 (18pp) [ DOI:10.1063/1.4819255 ]
arXiv:1303.5820(v2) [math-ph] [ pdf ]
27 pages, DPSU-13-1
typo (1303.5820(v2)):
* page 11, second step, 4-th line, last : ...(x), ==> ...(x)
* page 15, 7-th line (eq.(3.23), 2nd line from bottom): ...-(\sqrt ... ==> ...-\sqrt ...
* page 19, eq.(A.2) : \tilde{\delta}_{I} ==> \tilde{\delta}^{I}, \tilde{\delta}_{II} ==> \tilde{\delta}^{II}
* page 20, 1 line below eq.(A.8) : \tilde{\delta}_{I,II} ==> \tilde{\delta}^{I,II}

70.  Extensions of solvable potentials with finitely many discrete eigenstates

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 46 (2013) 235205 (15pp) [ DOI:10.1088/1751-8113/46/23/235205 ]
arXiv:1301.3980(v2) [math-ph] [ pdf ]
22 pages, 3 figure, DPSU-12-4, YITP-12-96

69.  Krein-Adler transformations for shape-invariant potentials and pseudo virtual states

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 46 (2013) 245201 (24pp) [ DOI:10.1088/1751-8113/46/24/245201 ]
arXiv:1212.6595(v2) [math-ph] [ pdf ]
33 pages, 1 figure, DPSU-12-3, YITP-12-85

J16.  シュレディンガー方程式と厳密解 〜解ける仕組みと新しい直交多項式の発見〜

解説記事
小竹 悟
数理科学 No.593 (2012年11月) 13-19 [ HP ]
原稿, 6ページ [ pdf ]

Schrodinger Equation and Exact Solutions - Solvable Mechanisms and Discovery of New Orthogonal Polynomials -

explanatory article
S. Odake
Suurikagaku 593 (Nov. 2012) 13-19 [ HP ]
manuscript, 6 pages [ pdf ]

68.  Multi-indexed Wilson and Askey-Wilson Polynomials

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 46 (2013) 045204 (22pp) [ DOI:10.1088/1751-8113/46/4/045204 ]
arXiv:1207.5584(v2) [math-ph] [ pdf ]
30 pages, DPSU-12-2, YITP-12-48
typo (1207.5584(v2)):
* (2.12) l.h.s : ...,gf_n] ==> ...,gf_n](x)
* (3.46) 1st line : P_{D,n}P_{D,n} ==> P_{D,n}P_{D,m}
* (A.5) 2nd line : P_{D} ==> P_{D,n}

67.  Multi-indexed (q-)Racah Polynomials

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 45 (2012) 385201 (21pp) [ DOI:10.1088/1751-8113/45/38/385201 ]
arXiv:1203.5868(v2) [math-ph] [ pdf, pdf(v1), comment ]
29 pages (v1:39 pages), DPSU-12-1, YITP-12-18
typo :
* 1203.5868(v2) (page 13, line 8 from the bottom), 1203.5868(v1) (page 10, line 5) :
  \hat{A}_{d_1}^{\dagger}\hat{A}_{d_1} ==> \hat{\mathcal{A}}_{d_1}^{\dagger}\hat{\mathcal{A}}_{d_1}

66.  Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials

S. Odake and R. Sasaki
Phys. Lett. B702 (2011) 164-170 [ DOI:10.1016/j.physletb.2011.06.075 ]
arXiv:1105.0508(v2) [math-ph] [ pdf ]
7 pages, 1 figure, DPSU-11-4, YITP-11-52
typo (1105.0508(v2)):
* 3rd paragraph in sec.4, line 3 : [4,20,7,8] ==> [4,20,7,8,34,35]
* page 2, right column, line 12: \log|(W ==> \log|W

65.  Discrete Quantum Mechanics

S. Odake and R. Sasaki
J. Phys. A: Math. Theor. 44 (2011) 353001 (47pp) [ DOI:10.1088/1751-8113/44/35/353001 ]
arXiv:1104.0473(v2) [math-ph] [ pdf ]
61 pages, 1 figure, DPSU-11-3, YITP-11-35
typo (1104.0473(v2)):
* eq.(2.132), c_1(\eta,\lambda) for H : -\frac{1}{2} ==> -\frac{\eta}{2}

64.  The Exceptional (X_{\ell}) (q)-Racah Polynomials

S. Odake and R. Sasaki
Prog. Theor. Phys. 125 (2011) 851-870 [ DOI:10.1143/PTP.125.851 ]
arXiv:1102.0812(v1) [math-ph] [ pdf ]
25 pages, DPSU-11-2, YITP-11-18
typo (1102.0812(v1)):
* eq.(6.12), 2nd line : dHdqH ==> dH,dqH
* 1 line above eq.(5.15) : are ==> is

63.  Dual Christoffel transformations

S. Odake and R. Sasaki
Prog. Theor. Phys. 126 (2011) 1-34 [ DOI:10.1143/PTP.126.1 ]
arXiv:1101.5468(v1) [math-ph] [ pdf, pdf(revised) ]
40 pages (revised: 41 pages), 4 figures, DPSU-11-1, YITP-11-7
typo (1101.5468(v1)):
* page 31, 2 line below eq.(A.33) : x=0,1,...,x_{max}^{\ell} ==> x=0,1,...,x_{max}^{\ell}+1,
* page 31, 2 line below eq.(A.33) : 0\leq x\leq x_{max} ==> 0\leq x\leq x_{max}^{\ell}+1

62.  A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell

S. Odake and R. Sasaki
J. Phys. A44 (2011) 195203 (14pp) [ DOI:10.1088/1751-8113/44/19/195203 ]
arXiv:1007.3800(v2) [math-ph] [ pdf ]
19 pages, DPSU-10-3, YITP-10-64

61.  Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations

S. Odake and R. Sasaki
J. Phys. A 43 (2010) 335201 (18pp) [ DOI:10.1088/1751-8113/43/33/335201 ]
arXiv:1004.0544(v2) [math-ph] [ pdf ]
24 pages, DPSU-10-2, YITP-10-19
typo (1004.0544(v2)):
* page 12, 1 line below eq.(3.1) : their the Schrodinger ==> their Schodinger
* page 20, 10-th line : from a known ones ==> from known ones
* page 23, ref.[30] : acad. ==> Acad.
* page 23, ref.[32] : Pramana ==> Pramana J. Phys.
remark:
* eqs.(2.73) and (2.74): It is assumed that 3F2 and 4F3 are finite sums.

60.  Modification of Crum's Theorem for `Discrete' Quantum Mechanics

L. García-Gutiérrez, S. Odake and R. Sasaki
Prog. Theor. Phys. 124 (2010) 1-26 [ DOI:10.1143/PTP.124.1 ]
arXiv:1004.0289(v2) [math-ph] [ pdf ]
31 pages, 2 figures, DPSU-10-1, YITP-10-15
typo (1004.0289(v2)):
* page 2, 6-th line from below : algebra of these algebras ==> algebra of these systems
* page 16, 9-th line : deleted level ==> deleted levels
* eq.(3.48) : V(x)^* ==> V^*(x) (2 places)

J15.  対称性 〜量子力学と群・代数の表現論〜

解説記事
小竹 悟
数理科学 No.561 (2010年3月) 44-50 [ HP ]
原稿, 6ページ [ pdf ]

Symmetry - Quantum Mechanics and Representation Theory of Groups and Algebras -

explanatory article
S. Odake
Suurikagaku 561 (March 2010) 44-50 [ HP ]
manuscript, 6 pages [ pdf ]

59.  Properties of the exceptional (X_{\ell}) Laguerre and Jacobi polynomials

C. -L. Ho, S. Odake and R. Sasaki
SIGMA 7 (2011) 107 (24pp) [ DOI:10.3842/SIGMA.2011.107 ]
arXiv:0912.5447(v4) [math-ph] [ pdf ]
30 pages, DPSU-09-7, YITP-09-70

58.  Another set of infinitely many exceptional (X_{\ell}) Laguerre polynomials

S. Odake and R. Sasaki
Phys. Lett. B684 (2010) 173-176 [ DOI:10.1016/j.physletb.2009.12.062 ]
arXiv:0911.3442(v1) [math-ph] [ pdf ]
4 pages, DPSU-09-6, YITP-09-74
typo (0911.3442(v1)):
* end of sec.2 : see a recent paper [12] ==> see a recent paper [6]

57.  Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials

S. Odake and R. Sasaki
J. Math. Phys. 51 (2010) 053513 (9pp) [ DOI:10.1063/1.3371248 ]
arXiv:0911.1585(v1) [math-ph] [ pdf ]
13 pages, DPSU-09-5, YITP-09-69

56.  Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials

S. Odake and R. Sasaki
Phys. Lett. B682 (2009) 130-136 [ DOI:10.1016/j.physletb.2009.10.078 ]
arXiv:0909.3668(v2) [math-ph] [ pdf ]
7 pages, DPSU-09-4, YITP-09-52

55.  Infinitely many shape invariant potentials and new orthogonal polynomials

S. Odake and R. Sasaki
Phys. Lett. B679 (2009) 414-417 [ DOI:10.1016/j.physletb.2009.08.004 ]
arXiv:0906.0142(v2) [math-ph] [ pdf ]
4 pages(REVTeX4), DPSU-09-3, YITP-09-36

54.  Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism

S. Odake and R. Sasaki
J. Math. Phys 51 (2010) 083502 (24pp) [ DOI:10.1063/1.3458866 ]
arXiv:0903.2604(v1) [math-ph] [ pdf ]
32 pages, DPSU-09-2, YITP-09-14

53.  Crum's Theorem for `Discrete' Quantum Mechanics

S. Odake and R. Sasaki
Prog. Theor. Phys 122 (2009) 1067-1079 [ DOI:10.1143/PTP.122.1067 ]
arXiv:0902.2593(v2) [math-ph] [ pdf ]
13 pages, DPSU-09-1, YITP-09-12

52.  Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states

S. Odake and R. Sasaki
Prog. Theor. Phys. 119 (2008) 663-700 [ DOI:10.1143/PTP.119.663 ]
arXiv:0802.1075(v1) [quant-ph] [ pdf ]
46 pages, 2 figures, DPSU-08-1, YITP-08-1

51.  Orthogonal Polynomials from Hermitian Matrices

S. Odake and R. Sasaki
J. Math. Phys. 49 (2008) 053503 (43pp) [ DOI:10.1063/1.2898695 ]
arXiv:0712.4106(v2) [math.CA] [ pdf ]
53 pages, DPSU-07-5, YITP-07-91
typo (0712.4106(v2)):
* eq.(5.55), LHS : \phi_0(x;\lambda) ==> \phi_0(x;\lambda)^2
* eq.(5.73), argument of R_n : \epsilon' (1+d+\eta(x;\lambda)) ==> 1+d+\epsilon' \eta(x;\lambda)
* eq.(5.73), last part : ...,dc^{-1}) ==> ...,dc^{-1}|q)
* eq.(5.80), last part : ...q^{-1}))(1+\tilde{d})) ==> ...q^{-1})(1+\tilde{d})))
* eq.(5.122) : B(...)=q^{-1} B(...), D(...)=q D(...) ==> B(...)=q^{-2} B(...), D(...)=D(...)
* eq.(5.210), 2nd eq. : d_n(\lambda)^2=... ==> d_n(\lambda)^2=q^n ...
* page 48, 2 lines below eq.(A.9) : the the ==> the
* page 49, 2nd line : the the ==> the
* page 53, ref.23, last line : 319324 ==> 319-324
* The dual q-Meixner polynomial in sec.5.2.4 and dual q-Charlier polynomial in sec.5.2.8 should be deleted because the hermiticity of the Hamiltonian is lost for these two cases. ==> See arXiv:1604.00714.

50.  q-oscillator from the q-Hermite Polynomial

S. Odake and R. Sasaki
Phys. Lett. B 663 (2008) 141-145 [ DOI:10.1016/j.physletb.2008.03.043 ]
arXiv:0710.2209(v2) [hep-th] [ pdf ]
12 pages, DPSU-07-4, YITP-07-64

49.  Multi-Particle Quasi Exactly Solvable Difference Equations

S. Odake and R. Sasaki
J. Math. Phys. 48 (2007) 122105 (8pp) [ DOI:10.1063/1.2818561 ]
arXiv:0708.0716(v1) [nlin.SI] [ pdf ]
12 pages, DPSU-07-3, YITP-07-44

48.  Interpolation of SUSY quantum mechanics

S. Odake, Y. Pehlivan and R. Sasaki
J. Phys. A 40 (2007)11973-11986 [ DOI:10.1088/1751-8113/40/39/017 ]
arXiv:0707.0314(v1) [math-ph] [ pdf ]
18 pages, DPSU-07-2, YITP-07-39

47.  Exact Heisenberg operator solutions for multi-particle quantum mechanics

S. Odake and R. Sasaki
J. Math. Phys. 48 (2007) 082106 (12pp) [ DOI:10.1063/1.2771544 ]
arXiv:0706.0768(v1) [quant-ph] [ pdf ]
17 pages, DPSU-07-1, YITP-07-26
typo (0706.0768(v1)):
* recursion ==> recurrence
* 2 lines above eq.(3.7) : an ==> any
* 1 line below eq.(3.33) : the the ==> the

J14.  CSM模型, RSvD模型の諸性質に関する研究

研究報告 (2007年2月)
小竹 悟
学部長裁量経費による助成研究報告書 (2007年?月) ?-?.
原稿, 2ページ [ pdf ]

Study on some properties of CSM and RSvD models

research report (February 2002)
S. Odake
Report on research funded by "Gakubucho Sairyo Keihi", 2007, ?-?.
manuscript, 2 pages [ pdf ]

J13.  Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics

研究会報告 (基研研究会「弦理論と場の量子論における新たな進展」(2006.9.12-16))
小竹 悟
素粒子論研究114巻 (2007) F69 [ DOI:10.24532/soken.114.6_F69 ] OA
原稿, 1ページ [ pdf ]

Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics

workshop report (September 2006)
S. Odake
Soryushiron Kenkyu 114 (2007) F69 [ DOI:10.24532/soken.114.6_F69 ] OA
manuscript, 1 page [ pdf ]

46.  Exact solution in the Heisenberg picture and annihilation-creation operators

S. Odake and R. Sasaki
Phys. Lett. B 641 (2006) 112-117 [ DOI:10.1016/j.physletb.2006.08.017 ]
arXiv:quant-ph/0605221(v2) [ pdf ]
10 pages, DPSU-06-2, YITP-06-24

45.  Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics

S. Odake and R. Sasaki
J. Math. Phys. 47 (2006) 102102 (33pp) [ DOI:10.1063/1.2349485 ]
arXiv:quant-ph/0605215(v1) [ pdf ]
43 pages, DPSU-06-1, YITP-06-23
typo (quant-ph/0605215(v1)):
* eq.(2.49) : C_n ==> C_k
* eq.(3.100), RHS : -2(\mathcal{H}_c^2+...) ==> -(2\mathcal{H}_c^2+...)
* eq.(3.105), RHS : -2(\mathcal{H}^2+...) ==> -(2\mathcal{H}^2+...)
* 1 line above eq.(C.14) : Askey-Wilson Hahn ==> Askey-Wilson

44.  Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials

S. Odake and R. Sasaki
Prog. Theor. Phys. 114 (2005) 1245-1260 [ DOI:10.1143/PTP.114.1245 ]
arXiv:hep-th/0512155(v1) [ pdf ]
16 pages, 1 figure, DPSU-05-2

44a.  Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics

S. Odake and R. Sasaki
Rokko Lectures in Mathematics (Kobe University) 18 (2005) 85-110 (Elliptic Integrable Systems, Eds. M. Noumi and K. Takasaki) [ISBN 4907719183] [ rlm18 ]
arXiv:hep-th/0505070(v1) [ pdf ]
30 pages, 1 figure, DPSU-05-1
typo (hep-th/0505070(v1)):
* eq.(109) : g_2 ==> g_2+\tfrac12
* 2 lines below eq.(110) : g_2 ==> g_2+\tfrac12
* 3 lines below eq.(10) : couplings ==> coupling
* 1 line below eq.(20) : couplings ==> coupling
* section 7, 2nd paragraph, 7-th line : without invariance ==> without shape invariance
* ref.[17] : Aemr ==> Amer

43.  Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials

S. Odake and R. Sasaki
J. Math. Phys. 46 (2005) 063513 (10pp) [ DOI:10.1063/1.1927080 ]
arXiv:hep-th/0410109(v2) [ pdf ]
14 pages, 1 figure, DPSU-04-4, YITP-04-60

42.  Shape Invariant Potentials in "Discrete Quantum Mechanics"

S. Odake and R. Sasaki
J. Nonlinear Math.Phys. 12 Supplement 1 (2005) 507-521 [ DOI:10.2991/jnmp.2005.12.s1.41 ]
arXiv:hep-th/0410102(v1) [ pdf ]
15 pages, 1 figure, DPSU-04-3, YITP-04-55

41.  Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems

S. Odake and R. Sasaki
J. Phys. A 37 (2004) 11401-11406 [ DOI:10.1088/0305-4470/37/47/009 ]
arXiv:hep-th/0407259(v1) [ pdf ]
9 pages, DPSU-04-2, YITP-04-41

40.  Equilibria of 'Discrete' Integrable Systems and Deformation of Classical Orthogonal Polynomials

S. Odake and R. Sasaki
J. Phys. A 37 (2004) 11841-11876 [ DOI:10.1088/0305-4470/37/49/006 ]
arXiv:hep-th/0407155(v2) [ pdf ]
45 pages, DPSU-04-1, YITP-04-36
typo (0407155(v2), J.Phys.A):
* eq.(2.19) (middle part) : \frac{(-x)^j}{r!} ==> \frac{(-x)^j}{j!}
* eq.(4.22) : \varepsilon=\frac{b}{a} ==> \varepsilon=\frac{a}{b}
* 1 line below (3.29) and (4.25) : \frac{\delta}{\varepsilon} ==> \delta\varepsilon
* 3 lines below (2.101) : 2^{-1}\schoose{2n-1}{n}^{-1} ==> \schoose{n-1/2}{n}^{-1}

J12.  Ruijsenaars-Schneider 模型の古典平衡点と変形された直交多項式

研究会報告 (基研研究会「場の理論 2004」(2004.7.13-16))
小竹 悟
素粒子論研究110巻 (2004) C19 [ DOI:10.24532/soken.110.3_C19 ] OA
原稿, 1ページ [ pdf ]

Classical Equilibrium Positions in Ruijsenaars-Schneider Models and Deformed Orthogonal Polynomials

workshop report (July 2004)
S. Odake
Soryushiron Kenkyu 110 (2004) C19 [ DOI:10.24532/soken.110.3_C19 ] OA
manuscript, 1 page [ pdf ]

J11.  Ruijsenaars 模型の古典平衡点と変形された直交多項式

研究会報告 (第21回代数的組合せ論シンポジウム (2004.6.28-30))
小竹 悟
第21回代数的組合せ論シンポジウム報告集 (2004年10月) 16-25 [ HP ]
原稿, 10ページ [ pdf ]

Classical Equilibrium Positions in Ruijsenaars Models and Deformed Orthogonal Polynomials

workshop report (June 2004)
S. Odake
Proceedings of the 21st Symposium on Algebraic Combinatorics, (October 2004) 16-25 [ HP ]
manuscript, 10 page [ pdf ]

J10.  Calogero-Moser 模型，Ruijsenaars-Schneider 模型の古典平衡点に付随する多項式

研究報告 (2004年4月)
小竹 悟
学部長裁量経費による助成研究報告書 (2004年5月) 10-12.
原稿, 3ページ [ pdf ]

Polynomials Associated with Classical Equilibrium Positions in Calogero-Moser and Ruijsenaars-Schneider Models

research report (April 2004)
S. Odake
Report on research funded by "Gakubucho Sairyo Keihi", May 2004, 10-12.
manuscript, 3 pages [ pdf ]

39.  Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems

S. Odake and R. Sasaki
J. Phys. A 35 (2002) 8283-8314 [ DOI:10.1088/0305-4470/35/39/312 ]
arXiv:hep-th/0206172(v1) [ pdf, poly.m ]
41 pages, DPSU-02-1, YITP-02-37. A Mathematica file ``poly.m" is attached.

38.  Comments on the Deformed W_N Algebra

S. Odake
Int. J. Mod. Phys. B16 (2002) 2055-2064 [ DOI:10.1142/S0217979202011792 ]
(Series on Advances in Statistical Mechanics Vol.15 Lattice Statistics and Mathematical Physics edited by J. H. H. Perk and M -L Ge, World Scientific 2002, 203-212. [ISBN 9812382038] [ DOI:10.1142/5136 ])
arXiv:math.QA/0111230(v1) [ pdf ]
10 pages, DPSU-01-2

37.  On Lepowsky-Wilson's {\mathcal Z}-algebra

Y. Hara, M. Jimbo, H. Konno, S. Odake and J. Shiraishi
Contemporary Mathematics 297 (2002) 143-149 [ DOI:10.1090/conm/297 ]
(Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory edited by S. Berman, P. Fendley, Y. -Z. Huang, K. Misra and B. Parshall)
arXiv:math.QA/0005203(v1) [ pdf ]
8 pages, DPSU-00-2

36.  Free Field Construction for the ABF Models in Regime II

M. Jimbo, H. Konno, S. Odake, Y. Pugai and J. Shiraishi
J. Stat. Phys. 102 (2001) 883-921 [ DOI:10.1023/A:1004807104626 ]
arXiv:math.QA/0001071(v2) [ pdf ]
36 pages, HU-IAS/K-8, DPSU-99-8, RIMS-1266

35.  Beyond CFT : Deformed Virasoro and Elliptic Algebras

S. Odake
Theoretical Physics at the End of the Twentieth Century (Lecture Notes of the CRM Summer School, Banff, Alberta) edited by Y. Saint-Aubin and L. Vinet, Springer 2002, 307-449. [ISBN 0387953116] [ amazon, amazon(jp) ]
arXiv:hep-th/9910226(v2) (See v2a) [ pdf, revised points ] [ pdf(v2a) ]
134 pages, DPSU-99-5
typo (9910226(v2a)):
* BRST Tyupin ==> Tyutin
* 1 line below eq.(2.5) : z^n w^m ==> z^{-n} w^{-m}

34.  Free Field Approach to the Dilute A_L Models

Y. Hara, M. Jimbo, H. Konno, S. Odake and J. Shiraishi
J. Math. Phys. 40 (1999) 3791-3826 [ DOI:10.1063/1.532927 ]
arXiv:math.QA/9902150(v1) [ pdf ]
43 pages, HU-IAS/K-7, DPSU-99-2

33.  Elliptic algebra U_{q,p}(\widehat{sl}_2): Drinfeld currents and vertex operators

M. Jimbo, H. Konno, S. Odake and J. Shiraishi
Comm. Math. Phys. 199 (1999) 605-647 [ DOI:10.1007/s002200050514 ]
arXiv:math.QA/9802002(v5) [ pdf ]
49 pages, HU-IAS/K-6, DPSU-98-2

32.  Quasi-Hopf twistors for elliptic quantum groups

M. Jimbo, H. Konno, S. Odake and J. Shiraishi
Transformation Groups 4 (1999) 303-327 [ DOI:10.1007/BF01238562 ]
arXiv:q-alg/9712029(v3) [ pdf ]
29 pages, DPSU-97-11

32a.  Quasi-Hopf twistors for elliptic quantum groups

Proceedings of the APCTP-Nankai Symposium (20-23 October 1998)
S. Odake
in Yang-Baxter Systems, Nonlinear Models and Their Applications, edited by B. K. Chung, Q-Han Park and C. Rim, World Scientific 2000, 173-182 [ISBN 9810241321] [ DOI:10.1142/9789814525985 ]
manuscript, 9 pages [ pdf ]

J9.  共形場理論を越えて -- 変形 Virasoro 代数が開く扉 --

粟田 英資, 久保 晴信, 守田 佳史, 小竹 悟, 白石 潤一
日本物理学会誌 第53巻第3号 (1998年3月) 170-180 (解説) [ DOI:10.11316/butsuri1946.53.170 ] OA

Beyond The Conformal Field Theory -- The Deformed Virasoro Algebra Opens A New Door --

H. Awata, H. Kubo, Y. Morita, S. Odake and J. Shiraishi
Butsuri(The Physical Society of Japan) Vol.53, No.3 (1998) 170-180 [ DOI:10.11316/butsuri1946.53.170 ] OA

31.  q-Difference Realization of U_q(sl(M|N)) and Its Application to Free Boson Realization of U_q(\widehat{sl}(2|1))

H. Awata, S. Odake and J. Shiraishi
Lett. Math. Phys. 42 (1997) 271-279 [ DOI:10.1023/A:1007308403718 ]
arXiv:q-alg/9701032(v1) [ pdf ]
8 pages, EFI-97-07, DPSU-97-1

30.  Virasoro-type Symmetries in Solvable Models

H. Awata, H. Kubo, S. Odake and J. Shiraishi
Proceedings of the Canada-China Meeting on Theoretical Physics edited by L. Lapointe, M.-L. Ge, Y. Saint-Aubin and L. Vinet, Les Publications CRM, Montreal, 2003, 154-188. [ISBN 2921120372] [ PM026 ]
arXiv:hep-th/9612233(v1) [ pdf ]
35 pages, EFI-96-44, DPSU-96-18, UT-764

29.  Quantum Deformation of the W_N Algebra

H. Awata, H. Kubo, S. Odake and J. Shiraishi
Proceedings of the Canada-China Meeting on Theoretical Physics edited by L. Lapointe, M.-L. Ge, Y. Saint-Aubin and L. Vinet, Les Publications CRM, Montreal, 2003, 112-130. [ISBN 2921120372] [ PM026 ]
arXiv:q-alg/9612001(v1) [ pdf ]
18 pages, EFI-96-45, DPSU-96-16, UT-762

28.  Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions

H. Awata, H. Kubo, Y. Morita, S. Odake and J. Shiraishi
Lett. Math. Phys. 41 (1997) 65-78 [ DOI:10.1023/A:1007321109584 ]
arXiv:q-alg/9604023(v1) [ pdf ]
9 pages, DPSU-96-7, UT-750

27.  Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms

T. Inami, S. Odake and Y-Z. Zhang
Nucl. Phys. B470[FS] (1996) 419-432 [ DOI:10.1016/0550-3213(96)00133-2 ]
arXiv:hep-th/9601049(v1) [ pdf ]
14 pages, YITP-96-1, DPSU-96-1

J8.  Virasoro 代数，W_N 代数，量子変形

研究会報告 (御岳サマースクール(1995年9月))
小竹 悟
??
原稿, 3ページ [ pdf ]

Virasoro Algebra, W_N Algebras and Quantum Deformation

workshop report (September 1995)
S. Odake
??
manuscript, 3 pages [ pdf ]

26.  Quantum {\cal W}_N Algebras and Macdonald Polynomials

H. Awata, H. Kubo, S. Odake and J. Shiraishi
Comm. Math. Phys. 179 (1996) 401-416 [ DOI:10.1007/BF02102595 ]
arXiv:q-alg/9508011(v4) [ pdf ]
17 pages, YITP/U-95-34, DPSU-95-9, UT-718

25.  A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions

J. Shiraishi, H. Kubo, H. Awata and S. Odake [ DOI:10.1007/BF00398297 ]
arXiv:q-alg/9507034(v5) [ pdf ]
15 pages, DPSU-95-5, UT-715

24.  Supersymmetric Extension of the Sine-Gordon Theory with Integrable Boundary Interaction

T. Inami, S. Odake and Y-Z. Zhang
Phys. Lett. B359 (1995) 118-124 [ DOI:10.1016/0370-2693(95)01072-X ]
arXiv:hep-th/9506157(v1) [ pdf ]
9 pages, YITP/K-1109, DPSU-95-2

23.  Integral Representations of the Macdonald Symmetric Polynomials

H. Awata, S. Odake and J. Shiraishi
Comm. Math. Phys. 179 (1996) 647-666 [ DOI:10.1007/BF02100101 ]
arXiv:q-alg/9506006(v4) [ pdf ]
21 pages, YITP/U-95-19, DPSU-95-1, UT-706

22.  Excited States of Calogero-Sutherland Model and Singular Vectors of the W_N Algebra

H. Awata, Y. Matsuo, S. Odake and J. Shiraishi
Nucl. Phys. B449 (1995) 347-374 [ DOI:10.1016/0550-3213(95)00286-2 ]
arXiv:hep-th/9503043(v4) [ pdf ]
29 pages, RIMS-1009, YITP/U-95-3, SULDP-1995-2

22a.  A Note on Calogero-Sutherland Model, W_n Singular Vectors and Generalized Matrix Models

H. Awata, Y. Matsuo, S. Odake and J. Shiraishi
Soryushiron Kenkyu 91 (1995) A69-A75 [ DOI:10.24532/soken.91.1_A69 ] OA
arXiv:hep-th/9503028(v2) [ pdf ]
9 pages

21.  Collective Field Theory, Calogero--Sutherland Model and Generalized Matrix Models

H. Awata, Y. Matsuo, S. Odake and J. Shiraishi
Phys. Lett. B347 (1995) 49-55 [ DOI:10.1016/0370-2693(95)00055-P ]
arXiv:hep-th/9411053(v3) [ pdf ]
13 pages, RIMS-997, YITP/U-94-29, SULDP-1994-8, UT-693

20.  Representation Theory of The W_{1+\infty} Algebra

H. Awata, M. Fukuma, Y. Matsuo and S. Odake
Prog. Theor. Phys. Supplement 118 (1995) 343-373 [ DOI:10.1143/PTPS.118.343 ]
arXiv:hep-th/9408158(v1) [ pdf ]
36 pages, RIMS-990, YITP/K-1087, YITP/U-94-25, SULDP-1994-7

"Representation Theory of W_{1+\infty} algebra," in Group Theoretical Methods in Physics edited by A. Arima, T. Eguchi and N. Nakanishi, World Scientific 1995, 335-338. [ISBN 9810220871] [ DOI:10.1142/9789814533386 ]

19.  Subalgebras of W_{1+\infty} and Their Quasifinite Representations

H. Awata, M. Fukuma, Y. Matsuo and S. Odake
J. Phys. A28 (1995) 105-112 [ DOI:10.1088/0305-4470/28/1/015 ]
arXiv:hep-th/9406111(v1) [ pdf ]
10 pages, RIMS-985, YITP/K-1076, YITP/U-94-22, SULDP-1994-4

18.  Character and Determinant Formulae of Quasifinite Representation of the W_{1+\infty} Algebra

H. Awata, M. Fukuma, Y. Matsuo and S. Odake
Comm. Math. Phys. 172 (1995) 377-400 [ DOI:10.1007/BF02099433 ]
arXiv:hep-th/9405093(v2) (<== There is something wrong with this web page.) [ pdf ]
34 pages, RIMS-982, YITP/K-1060, YITP/U-94-17, SULDP-1994-3 [ preprint(pdf) ]

17.  Quasifinite Highest Weight Modules over Super W_{1+\infty} Algebra

H. Awata, M. Fukuma, Y. Matsuo and S. Odake
Comm. Math. Phys. 170 (1995) 151-179 [ DOI:10.1007/BF02099443 ]
arXiv:hep-th/9404041(v1) (<== There is something wrong with this web page.) [ pdf ]
38 pages, YITP-K/1055, UT-670, SULDP-1994-2 [ preprint(pdf) ]

16.  Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels

H. Awata, M. Fukuma, Y. Matsuo and S. Odake
Phys. Lett. B332 (1994) 336-344 [ DOI:10.1016/0370-2693(94)91262-9 ]
arXiv:hep-th/9402001(v1) [ pdf ]
11 pages, YITP-K/1054, UT-669, SULDP-1994-1

15.  Eigensystem and Full Character Formula of the {\cal W}_{1+\infty} Algebra with c=1

H. Awata, M. Fukuma, S. Odake and Y. -H. Quano
Lett. Math. Phys. 31 (1994) 289-298 [ DOI:10.1007/BF00762791 ]
arXiv:hep-th/9312208(v2) [ pdf ]
12 pages, RIMS-959, YITP-K/1049, SULDP-1993-1

J7.  場の理論的方法によるスピン鎖

研究会報告 (基研研究会「低次元系の物性と場の理論」(1993.9.20-22))
小竹 悟
素粒子論研究88巻 (1994) E42-E47 [ DOI:10.24532/soken.88.5_E42 ] OA
物性研究61巻 (1994) 648-653 [ HP ] OA
原稿, 6ページ [ pdf ]

Spin Chain by Field Theoretical Method

Proceedings (September 1993)
S. Odake
Soryushiron Kenkyu 88 (1994) E42-E47 [ DOI:10.24532/soken.88.5_E42 ] OA
Bussei Kenkyu 61 (1994) 648-653 [ HP ] OA
manuscript, 6 pages [ pdf ]

14.  Heisenberg realization for U_q(sl_n) on the flag manifold

H. Awata, M. Noumi and S. Odake
Lett. Math. Phys. 30 (1994) 35-43 [ DOI:10.1007/BF00761420 ]
arXiv:hep-th/9306010(v2) [ pdf ]
10 pages, RIMS-920, YITP-K/1016

13.  Free Boson Realization of U_q(\widehat{sl}_N)

H. Awata, S. Odake and J. Shiraishi
Comm. Math. Phys. 162 (1994) 61-83 [ DOI:10.1007/BF02105187 ]
arXiv:hep-th/9305146(v1) [ pdf ]
24 pages, RIMS-924, YITP-K/1018

12.  Free Boson Representation of U_q(\widehat{sl}_3)

H. Awata, S. Odake and J. Shiraishi
Lett. Math. Phys. 30 (1994) 207-216 [ DOI:10.1007/BF00805853 ]
arXiv:hep-th/9305017(v1) [ pdf ]
12 pages, RIMS-920, YITP-K/1017

J6.  スピン１XXZ鎖の連続極限

素粒子奨学生応募論文
小竹 悟
素粒子論研究87巻 (1993) 107-119 [ DOI:10.24532/soken.87.1_107 ] OA

Continuum Limit of Spin 1 XXZ Chain

Soryushi scholarship application paper
S. Odake
Soryushiron Kenkyu 87 (1993) 107-119 [ DOI:10.24532/soken.87.1_107 ] OA

J5.  スピン鎖の連続極限

研究会報告
小竹 悟
??
原稿, 15ページ [ pdf ]

Continuum Limit of Spin Chains

workshop report
S. Odake
??
manuscript, 15 pages [ pdf ]

11.  Continuum Limit of Spin-1 Chain

T. Inami and S. Odake
Phys. Rev. Lett. 70 (1993) 2016-2019 [ DOI:10.1103/PhysRevLett.70.2016 ]
arXiv:hep-th/9209019(v2) [ pdf ]
10 pages, YITP/K-987

"Field Theory Limit of Spin-1 Chain,"
in Current Topics in Theoretical Physics edited by Y. M. Cho, World Scientific 1994, 113-124. [ISBN 9810220421] [ DOI:10.1142/9789814533577 ]

10.  Unitary Representations of W Infinity Algebras

S. Odake
Int. J. Mod. Phys. A7 (1992) 6339-6355 [ DOI:10.1142/S0217751X9200288X ]
arXiv:hep-th/9111058(v1) [ pdf ]
20 pages, YITP/K-955

J4.  W 無限大代数のユニタリ表現

素粒子奨学生応募論文
小竹 悟
素粒子論研究85巻 (1992) 237-254 [ DOI:10.24532/soken.85.4_237 ] OA

Unitary Representations of W Infinify algebras

Soryushi scholarship application paper
S. Odake
Soryushiron Kenkyu 85 (1992) 237-254 [ DOI:10.24532/soken.85.4_237 ] OA

9.  Two Matrix Model and Minimal Unitary Model

S. Odake
Phys. Lett. B269 (1991) 300-304 [ DOI:10.1016/0370-2693(91)90174-O ]
There are many typos by the publisher. See the preprint for correct formulas.
preprint, 12 pages, UT-578 [ pdf ]; pubilshed version, 9 pages [ pdf ]

8.  W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry

S. Odake and T. Sano
Phys. Lett. B258 (1991) 369-374 [ DOI:10.1016/0370-2693(91)91101-Z ]
preprint, 10 pages, UT-569 (October 1990) [ pdf ]

8a.  Comments on the W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry

S. Odake and T. Sano
KEK Proceedings 91-6 (1991) 80-94
manuscript, 15 pages [ pdf ]

7.  Nonperturbative Analysis of Three Matrix Model

H. Kunitomo and S. Odake
Phys. Lett. B247 (1990) 57-63 [ DOI:10.1016/0370-2693(90)91049-H ]
preprint, 13 pages, UT-558 (February 1990) [ pdf ]

6.  c=3d Conformal Algebra with Extended Supersymmetry

S. Odake
Mod. Phys. Lett. A5 (1990) 561-580 [ DOI:10.1142/S0217732390000640 ]
preprint, 29 pages, UT-551 (September 1989) [ pdf ]

6a.  c=3d Algebra

S. Odake
KEK report 89-22 (1990) 133-142 (Proceedings of the Workshop "Topology, Field Theory and Superstring") [ 89-22 ]
manuscript, 10 pages [ pdf ]

5.  Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification

S. Odake
Int. J. Mod. Phys. A5 (1990) 897-914 [ DOI:10.1142/S0217751X90000428 ]
preprint, 24 pages, UT-543 (April 1989) [ pdf ]

J3.  [博士論文](東京大学, 1988年12月)
  超共形代数とその拡張について

小竹 悟  [ 原稿(pdf) ]
素粒子論研究78巻 (1989) 201-260 [ DOI:10.24532/soken.78.6_201 ] OA  [ 原稿(pdf) ](<== 新しい結果を追加)

[PhD thesis] (Tokyo University, December 1988)
Super Conformal Algebra and its Extensions

S. Odake  [ manuscript(pdf) ]
Soryushiron Kenkyu 78 (1989) 201-260 [ DOI:10.24532/soken.78.6_201 ] OA  [ manuscript(pdf) ](<== new results are added)

4.  Extension of N=2 Superconformal Algebra and Calabi-Yau Compactification

S. Odake
Mod. Phys. Lett. A4 (1989) 557-568 [ DOI:10.1142/S021773238900068X ]
preprint, 14 pages, UT-537 (September 1988) [ pdf ]

3.  Operator Product Expansion Coefficients in N=1 Superconformal Theory and Slightly Relevant Perturbation

Y. Kitazawa, N. Ishibashi, A. Kato, K. Kobayashi, Y. Matsuo and S. Odake
Nucl. Phys. B306 (1988) 425-444 [ DOI:10.1016/0550-3213(88)90700-6 ]
preprint, 26+2 pages, UT-522 (December 1987) [ KEK library scan(pdf) ]

2.  Fermionic Construction of N=0,1,2 (Super)Conformal Algebras

K. Kobayashi and S. Odake
Mod. Phys. Lett. A3 (1988) 773-781 [ DOI:10.1142/S0217732388000933 ]
preprint, 12 pages, UT-514 (July 1987) [ scan(pdf) ]

2a.  Fermionic Construction of N=0,1,2 (Super)Conformal Algebras

K. Kobayashi and S. Odake
Proceedings of 7th INS Winter Seminar on Superstrings, Composite Models and Anomaly Related Problems (1988) 199-211 [ 784291 ]
manuscript, 12 pages [ scan(pdf) ]

1.  Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude

A. Kato, Y. Matsuo and S. Odake
Phys. Lett. B179 (1986) 241-246 [ DOI:10.1016/0370-2693(86)90573-3 ]
preprint, 13 pages, 2 figures, UT-489 (July 1986) [ scan(pdf) ]

J2.  Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude

研究会報告 (1986年12月)
加藤 晃史，松尾 泰，小竹 悟
素粒子論研究75巻 (1987) E3-E5 [ DOI:10.24532/soken.75.5_E3_2 ] OA

Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude

Proceedings (December 1986)
A. Kato, Y. Matsuo and S. Odake
Soryushiron Kenkyu 75 (1987) E3-E5 [ DOI:10.24532/soken.75.5_E3_2 ] OA

J1.  [修士論文](東京大学, 1986年1月)
  非線型シグマ模型と共形不変性

小竹 悟
原稿, 164+3ページ [ スキャン(pdf) ]

[Master thesis](Tokyo University, January 1986)
Non-linear Sigma Models and Conformal Invariance

S. Odake
manuscript, 164+3 page [ scan(pdf) ]
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