小竹 悟 (オダケ サトル)
学術研究院 理工学域 理学系
理学部 理学科 物理学コース
教授
研究者情報
経歴
学歴
研究活動情報
論文
- ``Diophantine'' and Factorisation Properties of Finite Orthogonal Polynomials in the Askey Scheme
S.Odake and R.Sasaki
Journal of Difference Equations and Applications, 30, 820-848, 2024年, 査読有り
- Another Type of Forward and Backward Shift Relations for Orthogonal Polynomials in the Askey Scheme
S.Odake
Journal of Mathematical Analysis and Application, 540(1), 128591, 2024年, 査読有り - Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts
S.Odake
Journal of Mathematical Physics, 64(5), 53503, 2023年, 査読有り - New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations
S.Odake
Progress of Theoretical and Experimental Physics, 2023(7), 073A01, 2023年, 査読有り - Free Oscillator Realization of Laguerre Polynomial
S.Odake
Theoretical and Mathematical Physics, 210, 1-7, 2022年, 査読有り - Markov Chains Generated by Convolutions of Orthogonality Measures
S.Odake and R.Sasaki
Journal of Physics, 55(27), 275201, 2022年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types
S.Odake
Journal of Mathematical Physics, 61(5), 053505, 2020年, 査読有り - Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems
S.Odake
Journal of Physics, A53(36), 365202, 2020年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and q-Racah types
S.Odake
Journal of Mathematical Physics, 60(2), 023508, 2019年, 査読有り - Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types
S.Odake
Progress of Theoretical and Experimental Physics, 2019(12), 123A01, 2019年, 査読有り - Dual Polynomials of the Multi-Indexed (q-)Racah Orthogonal Polynomials
S.Odake
Progress of Theoretical and Experimental Physics, 2018(7), 073A02, 2018年, 査読有り - Orthogonal polynomials from Hermitian matrices. II
S.Odake and R.Sasaki
Journal of Mathematical Physics, 59(1), 013504, 2018年, 査読有り
- Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials
S.Odake and R.Sasaki
SIGMA, 13, 020, 2017年, 査読有り - New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
S.Odake
Progress of Theoretical and Experimental Physics, 2017(5), 053A01, 2017年, 査読有り - Casoratian identities for the discrete orthogonal polynomials in discrete quantum mechanics with real shifts
S.Odake
Progress of Theoretical and Experimental Physics, 2017(12), 123A02, 2017年, 査読有り - Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
S.Odake and R.Sasaki
Journal of Physics, 50(16), 165204, 2016年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
S.Odake
Journal of Mathematical Physics, 57(2), 023514, 2016年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
S.Odake
Journal of Mathematical Physics, 57(11), 113503, 2016年, 査読有り - 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, 71(3), 156-163, 2016年, 査読有り - Casoratian Identities for the Wilson and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Approximation Theory, 193, 184-209, 2015年, 査読有り - Reflectionless Potentials for Difference Schr\"odinger Equations
S.Odake and R.Sasaki
Journal of Physics, A48(11), 115204, 2015年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
S.Odake
Journal of Mathematical Physics, 56(5), 053506, 2015年, 査読有り - Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
S.Odake and R.Sasaki
Journal of Mathematical Physics, 56(7), 073502, 2015年, 査読有り - Equivalences of the multi-indexed orthogonal polynomials
S.Odake
Journal of Mathematical Physics, 55, 013502, 2014年, 査読有り - Multi-indexed Wilson and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Physics, A46, 045204, 2013年, 査読有り - Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
S.Odake and R.Sasaki
Journal of Physics, A46, 245201, 2013年, 査読有り - Extensions of solvable potentials with finitely many discrete eigenstates
S.Odake and R.Sasaki
Journal of Physics, A46, 235205, 2013年, 査読有り - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
S.Odake
Journal of Mathematical Physics, 54, 083506, 2013年, 査読有り - Non-polynomial extensions of solvable potentials a la Abraham-Moses
S.Odake and R.Sasaki
Journal of Mathematical Physics, 54, 102106, 2013年, 査読有り - Multi-indexed (q-)Racah Polynomials
S.Odake and R.Sasaki
Journal of Physics, A45, 385201, 2012年, 査読有り - Properties of the exceptional (X-l) Laguerre and Jacobi polynomials
C.-L.Ho, S.Odake and R.Sasaki
SIGMA, 7, 107, 2011年, 査読有り - Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
S.Odake and R.Sasaki
Physics Letters, B702, 164, 2011年, 査読有り - A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell
S.Odake and R.Sasaki
Journal of Physics, A44, 195203, 2011年, 査読有り - Dual Christoffel transformations
S.Odake and R.Sasaki
Progress of Theoretical Physics, 126, 1, 2011年, 査読有り - The Exceptional (X_{\ell}) (q)-Racah Polynomials
S.Odake and R.Sasaki
Progress of Theoretical Physics, 125(5), 851, 2011年, 査読有り - Discrete Quantum Mechanics
S.Odake and R.Sasaki
Journal of Physics, A44, 353001, 2011年, 査読有り - Another set of infinitely many exceptional ($X_{\ell}$) Laguerre polynomials
S.Odake and R.Sasaki
Physics Letters, B684, 173-176, 2010年, 査読有り - Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
S.Odake and R.Sasaki
Journal of Mathematical Physics, 51, 053513, 2010年, 査読有り - Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
S.Odake and R.Sasaki
Journal of Mathematical Physics, 51, 083502, 2010年, 査読有り - Modification of Crum's Theorem for `Discrete' Quantum Mechanics
L..Garcia-Gutierrez, S.Odake and R.Sasaki
Progress of Theoretical Physics, 124(1), 1-26, 2010年, 査読有り - Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
S.Odake and R.Sasaki
Journal of Physics, A43, 335201, 2010年, 査読有り - Infinitely many shape invariant potentials and new orthogonal polynomials
S.Odake and R.Sasaki
Physics Letters, B679, 414, 2009年, 査読有り - 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
Physics Letters, B682, 130, 2009年, 査読有り - Crum's Theorem for `Discrete' Quantum Mechanics
S.Odake and R.Sasaki
Progress of Theoretical Physics, 122(5), 1067-1079, 2009年, 査読有り - q-oscillator from the q-Hermite Polynomial
S.Odake and R.Sasaki
Physics Letters, B663(1-2), 141-145, 2008年, 査読有り - Orthogonal Polynomials from Hermitian Matrices
S.Odake and R.Sasaki
Journal of Mathematical Physics, 49(5), 053503, 2008年, 査読有り - Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
S.Odake and R.Sasaki
Progress of Theoretical Physics, 119(4), 663-700, 2008年 - Exact Heisenberg operator solutions for multi-particle quantum mechanics
S.Odake and R.Sasaki
Journal of Mathematical Physics, 48(8), 082106, 2007年, 査読有り - Interpolation of SUSY quantum mechanics
S.Odake, Y.Pehlivan and R.Sasaki
Journal of Physics, A40(39), 11973-11986, 2007年, 査読有り - Multi-Particle Quasi Exactly Solvable Difference Equations
S.Odake and R.Sasaki
Journal of Mathematical Physics, 48(12), 122105, 2007年, 査読有り - Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
S.Odake and R.Sasaki
Journal of Mathematical Physics, 47(10), 102102 (33pages), 2006年, 査読有り - Exact solution in the Heisenberg picture and annihilation-creation operators
S.Odake and R.Sasaki
Physics Letters, B641(1), 112-117, 2006年, 査読有り - Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
S.Odake and R.Sasaki
Rokko Lectures in Mathematics (Kobe University) (Elliptic Integrable Systems, Eds. M.Noumi and K.Takasaki), 18, 85-110, 2005年, 査読有り - Shape Invariant Potentials in ``Discrete Quantum Mechanics"
S.Odake and R.Sasaki
Journal of Nonlinear Mathematical Physics, 12 Supplement 1, 507-521, 2005年, 査読有り - Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Mathematical Physics, 46(6), 063513 (10pages), 2005年, 査読有り - Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
S.Odake and R.Sasaki
Progress of Theoretical Physics, 114(6), 1245-1260, 2005年, 査読有り - Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
S.Odake and R.Sasaki
Journal of Physics, A37(49), 11841-11876, 2004年, 査読有り - Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
S.Odake and R.Sasaki
Journal of Physics, A37(47), 11401-11406, 2004年, 査読有り - 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, 112-130, 2003年 - 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, 154-188, 2003年 - On Lepowsky-Wilson's {\cal Z}-algebra
Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Contemporary Mathematics, 297, 143-149, 2002年, 査読有り - 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, 307-449, 2002年 - Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems
S.Odake and R.Sasaki
Journal of Physics, A35(39), 8283-8314, 2002年, 査読有り - Comments on the deformed W-N algebra
S.Odake
International Journal of Modern Physics B, 16(14-15), 2055-2064, 2002年, 査読有り - Free Field Construction for the ABF Models in Regime II
M.Jimbo, H.Konno, S.Odake, Y.Pugai and J.Shiraishi
Journal of Statistical Physics, 102(3-4), 883-921, 2001年, 査読有り - Quasi-Hopf twistors for elliptic quantum groups
S.Odake
`Yang-Baxter Systems, Nonlinear Models and Their Applications' edited by B.K. Chung, Q-Han Park and C.Rim, 173-182, 2000年 - Quasi-Hopf twistors for elliptic quantum groups
M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Transformation Groups, 4, 303-327, 1999年, 査読有り - Elliptic algebra U_{q,p}(\widehat{sl}_2) : Drinfeld currents and vertex operators
M.Jimbo, H.Konno, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 199, 605-647, 1999年, 査読有り - Free Field Approach to the Dilute A_L Models
Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Journal of Mathematical Physics, 40, 3791-3826, 1999年, 査読有り - 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, 53(3), 170-180, 1998年 - 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
LETTERS IN MATHEMATICAL PHYSICS, 41, 65-78, 1997年, 査読有り - 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
LETTERS IN MATHEMATICAL PHYSICS, 42, 271-279, 1997年, 査読有り - Integral Representations of the Macdonald Symmetric Polynomials
H.Awata, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179, 647-666, 1996年, 査読有り - A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
J.Shiraishi, H.Kubo, H.Awata and S.Odake
LETTERS IN MATHEMATICAL PHYSICS, 38, 33-51, 1996年, 査読有り - Quantum {\cal W}_N Algebras and Macdonald Polynomials
H.Awata, H.Kubo, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179, 401-416, 1996年, 査読有り - 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
Nuclear Physics, B470[FS], 419-432, 1996年, 査読有り - Quasifinite Highest Weight Modules over Super W_{1+\infty} Algebra
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 170, 151-179, 1995年, 査読有り - Character and Determinant Formulae of Quasifinite Representation of the W_{1+\infty} Algebra
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 172, 377-400, 1995年, 査読有り - Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
Journal of Physics, A28, 105-112, 1995年, 査読有り - Representation Theory of The W_{1+\infty} Algebra
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
Progress of Theoretical Physics Proceedings Supplement, 118, 343-373, 1995年, 査読有り - Collective Field Theory, Calogero--Sutherland Model and Generalized Matrix Models
H.Awata, Y.Matsuo, S.Odake and J.Shiraishi
Physics Letters, B347, 49-55, 1995年, 査読有り - Excited States of Calogero-Sutherland Model and Singular Vectors of the W_N Algebra
H.Awata, Y.Matsuo, S.Odake and J.Shiraishi
Nuclear Physics, B449, 347-374, 1995年, 査読有り - 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(Kyoto), 91, A69-A75, 1995年 - Supersymmetric Extension of the Sine-Gordon Theory with Integrable Boundary Interaction
T.Inami, S.Odake and Y-Z.Zhang
Physics Letters, B359, 118-124, 1995年, 査読有り - Representation Theory of $W_{1+\infty}$ algebra
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
`Group Theoretical Methods in Physics' edited by A.Arima, T.Eguchi and N. Nakanishi, 335-338, 1995年 - Free Boson Representation of U_q(\widehat{sl}_3)
H.Awata, S.Odake and J.Shiraishi
LETTERS IN MATHEMATICAL PHYSICS, 30, 207-216, 1994年, 査読有り - Free Boson Realization of U_q(\widehat{sl}_N)
H.Awata, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 162, 61-83, 1994年, 査読有り - Heisenberg realization for U_q(sl_n) on the flag manifold
H.Awata, M.Noumi and S.Odake
LETTERS IN MATHEMATICAL PHYSICS, 30, 35-43, 1994年, 査読有り - 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
LETTERS IN MATHEMATICAL PHYSICS, 31, 289-298, 1994年, 査読有り - Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
H.Awata, M.Fukuma, Y.Matsuo and S.Odake
Physics Letters, B332, 336-344, 1994年, 査読有り - 場の理論的方法によるスピン鎖
小竹 悟
物性研究, 61, 648-653, 1994年 - Field Theory Limit of Spin-1 Chain
T.Inami and S.Odake
`Current Topics in Theoretical Physics' edited by Y.M.Cho, 113-124, 1994年 - Continuum Limit of Spin-1 Chain
T.Inami and S.Odake
Physical Review Letters, 70, 2016-2019, 1993年, 査読有り - スピン１XXZ鎖の連続極限
小竹 悟
素粒子論研究, 87, 107-119, 1993年 - Unitary Representations of $W$ Infinity Algebras
S.Odake
International Journal of Modern Physics, A7, 6339-6355, 1992年, 査読有り - W 無限大代数のユニタリ表現
小竹 悟
素粒子論研究, 85, 237-254, 1992年 - W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry
S.Odake and T.Sano
Physics Letters, B258, 369-374, 1991年, 査読有り - Comments on the $W_{1+\infty}$ and Super $W_{\infty}$ Algebras with $SU(N)$ Symmetry
S.Odake and T.Sano
KEK Proceedings, 91-6, 80-94, 1991年 - Two Matrix Model and Minimal Unitary Model
S.Odake
Physics Letters, B269, 300-304, 1991年, 査読有り - Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
S.Odake
International Journal of Modern Physics, A5, 897-914, 1990年, 査読有り - c=3d Conformal Algebra with Extended Supersymmetry
S.Odake
Modern Physics Letters, A5, 561-580, 1990年, 査読有り - c=3d Algebra
S.Odake
Proceedings of the Workshop ``Topology, Field Theory and Superstring" KEK report, 89-22, 133-142, 1990年 - Nonperturbative Analysis of Three Matrix Model
H.Kunitomo and S.Odake
Physics Letters, B247, 57-63, 1990年, 査読有り - Extension of N=2 Superconformal Algebra and Calabi-Yau Compactification
S.Odake
Modern Physics Letters, A4, 557-568, 1989年, 査読有り - 超共形代数とその拡張について
小竹 悟
素粒子論研究, 78, 201-260, 1989年 - Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
K.Kobayashi and S.Odake
Modern Physics Letters, A3, 773-781, 1988年, 査読有り - 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, 199-211, 1988年 - 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
Nuclear Physics, B306, 425-444, 1988年, 査読有り - Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
加藤 晃史，松尾 泰，小竹 悟
素粒子論研究, 75, e3-E5, 1987年 - Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
A.Kato, Y.Matsuo and S.Odake
Physics Letters, B179, 241-246, 1986年, 査読有り
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- 物理と対称性
信州大学 - 物理数学Ⅰ
信州大学 - 物理数学Ⅱ
信州大学 - 物理数学Ⅲ
信州大学 - 力学Ⅲ
信州大学 - 力学
信州大学 - 物理学演習III（半分）
信州大学 - 物理学演習Ⅳ（半分）
信州大学 - 力学Ⅲ演習
信州大学 - 物理数学Ⅱ演習
信州大学 - 物理学演習Ⅰ(一部分）
信州大学 - 物理学演習Ⅱ(一部分）
信州大学 - 物理へのいざない（一部分）
信州大学 - 新入生ゼミナール
信州大学 - アドバンスゼミ（一部分）
信州大学 - アドバンス演習実験実習Ⅰ（一部分）
信州大学 - アドバンス演習実験実習Ⅱ（一部分）
信州大学 - アドバンス演習実験実習Ⅲ（一部分）
信州大学 - アドバンス演習実験実習Ⅳ（一部分）
信州大学 - 先端科学特別講義（一部分）
信州大学 - 物質基礎科学セミナー
信州大学 - 宇宙物理学（一部分）
信州大学 - 物理学最前線（一部分）
信州大学 - 物理学概論
信州大学 - 量子力学特論Ⅰ
信州大学 - 物理数学
信州大学 - 物理数学演習
信州大学 - 線形代数
信州大学 - 線形代数学A
信州大学 - 線形代数学B
信州大学 - 数学概論Ⅰ
信州大学 - 「体験する力学ー物理学の考え方と数理ー」ゼミ
信州大学 - 物理数学Ⅲ演習
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信州大学 - 物理学ⅠC
信州大学 - 量子力学Ⅱ演習
信州大学 - 量子力学Ⅲ演習
信州大学 - 素粒子物理学（一部分）
信州大学
