ODAKE SATORU
Academic Assembly, School of Science and Technology, Institute of Science
Faculty of Science Department of Science Course of Physics
Professor
Researcher Information
Field Of Study
Research activity information
Paper
- ``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, Refereed
- 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, Refereed - 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, Refereed - 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, Refereed - Free Oscillator Realization of Laguerre Polynomial
S.Odake
Theoretical and Mathematical Physics, 210, 1-7, 2022, Refereed - Markov Chains Generated by Convolutions of Orthogonality Measures
S.Odake and R.Sasaki
Journal of Physics, 55(27), 275201, 2022, Refereed - 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, Refereed - Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems
S.Odake
Journal of Physics, A53(36), 365202, 2020, Refereed - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and q-Racah types
S.Odake
Journal of Mathematical Physics, 60(2), 023508, 2019, Refereed - 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, Refereed - Dual Polynomials of the Multi-Indexed (q-)Racah Orthogonal Polynomials
S.Odake
Progress of Theoretical and Experimental Physics, 2018(7), 073A02, 2018, Refereed - Orthogonal polynomials from Hermitian matrices. II
S.Odake and R.Sasaki
Journal of Mathematical Physics, 59(1), 013504, 2018, Refereed
- Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials
S.Odake and R.Sasaki
SIGMA, 13, 020, 2017, Refereed - 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, Refereed - 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, Refereed - Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
S.Odake and R.Sasaki
Journal of Physics, 50(16), 165204, 2016, Refereed - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
S.Odake
Journal of Mathematical Physics, 57(2), 023514, 2016, Refereed - 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, Refereed - 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, Refereed - Casoratian Identities for the Wilson and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Approximation Theory, 193, 184-209, 2015, Refereed - Reflectionless Potentials for Difference Schr\"odinger Equations
S.Odake and R.Sasaki
Journal of Physics, A48(11), 115204, 2015, Refereed - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
S.Odake
Journal of Mathematical Physics, 56(5), 053506, 2015, Refereed - 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, Refereed - Equivalences of the multi-indexed orthogonal polynomials
S.Odake
Journal of Mathematical Physics, 55, 013502, 2014, Refereed - Multi-indexed Wilson and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Physics, A46, 045204, 2013, Refereed - Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
S.Odake and R.Sasaki
Journal of Physics, A46, 245201, 2013, Refereed - Extensions of solvable potentials with finitely many discrete eigenstates
S.Odake and R.Sasaki
Journal of Physics, A46, 235205, 2013, Refereed - Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
S.Odake
Journal of Mathematical Physics, 54, 083506, 2013, Refereed - Non-polynomial extensions of solvable potentials a la Abraham-Moses
S.Odake and R.Sasaki
Journal of Mathematical Physics, 54, 102106, 2013, Refereed - Multi-indexed (q-)Racah Polynomials
S.Odake and R.Sasaki
Journal of Physics, A45, 385201, 2012, Refereed - Properties of the exceptional (X-l) Laguerre and Jacobi polynomials
C.-L.Ho, S.Odake and R.Sasaki
SIGMA, 7, 107, 2011, Refereed - Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
S.Odake and R.Sasaki
Physics Letters, B702, 164, 2011, Refereed - 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, Refereed - Dual Christoffel transformations
S.Odake and R.Sasaki
Progress of Theoretical Physics, 126, 1, 2011, Refereed - The Exceptional (X_{\ell}) (q)-Racah Polynomials
S.Odake and R.Sasaki
Progress of Theoretical Physics, 125(5), 851, 2011, Refereed - Discrete Quantum Mechanics
S.Odake and R.Sasaki
Journal of Physics, A44, 353001, 2011, Refereed - Another set of infinitely many exceptional ($X_{\ell}$) Laguerre polynomials
S.Odake and R.Sasaki
Physics Letters, B684, 173-176, 2010, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
S.Odake and R.Sasaki
Journal of Physics, A43, 335201, 2010, Refereed - Infinitely many shape invariant potentials and new orthogonal polynomials
S.Odake and R.Sasaki
Physics Letters, B679, 414, 2009, Refereed - 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, Refereed - Crum's Theorem for `Discrete' Quantum Mechanics
S.Odake and R.Sasaki
Progress of Theoretical Physics, 122(5), 1067-1079, 2009, Refereed - q-oscillator from the q-Hermite Polynomial
S.Odake and R.Sasaki
Physics Letters, B663(1-2), 141-145, 2008, Refereed - Orthogonal Polynomials from Hermitian Matrices
S.Odake and R.Sasaki
Journal of Mathematical Physics, 49(5), 053503, 2008, Refereed - 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 - Exact Heisenberg operator solutions for multi-particle quantum mechanics
S.Odake and R.Sasaki
Journal of Mathematical Physics, 48(8), 082106, 2007, Refereed - Interpolation of SUSY quantum mechanics
S.Odake, Y.Pehlivan and R.Sasaki
Journal of Physics, A40(39), 11973-11986, 2007, Refereed - Multi-Particle Quasi Exactly Solvable Difference Equations
S.Odake and R.Sasaki
Journal of Mathematical Physics, 48(12), 122105, 2007, Refereed - 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, Refereed - Exact solution in the Heisenberg picture and annihilation-creation operators
S.Odake and R.Sasaki
Physics Letters, B641(1), 112-117, 2006, Refereed - 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, Refereed - Shape Invariant Potentials in ``Discrete Quantum Mechanics"
S.Odake and R.Sasaki
Journal of Nonlinear Mathematical Physics, 12 Supplement 1, 507-521, 2005, Refereed - Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
S.Odake and R.Sasaki
Journal of Mathematical Physics, 46(6), 063513 (10pages), 2005, Refereed - 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, Refereed - Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
S.Odake and R.Sasaki
Journal of Physics, A37(49), 11841-11876, 2004, Refereed - Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
S.Odake and R.Sasaki
Journal of Physics, A37(47), 11401-11406, 2004, Refereed - 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 - 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 - On Lepowsky-Wilson's {\cal Z}-algebra
Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Contemporary Mathematics, 297, 143-149, 2002, Refereed - 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 - Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems
S.Odake and R.Sasaki
Journal of Physics, A35(39), 8283-8314, 2002, Refereed - Comments on the deformed W-N algebra
S.Odake
International Journal of Modern Physics B, 16(14-15), 2055-2064, 2002, Refereed - 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, Refereed - 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 - Quasi-Hopf twistors for elliptic quantum groups
M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Transformation Groups, 4, 303-327, 1999, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - Integral Representations of the Macdonald Symmetric Polynomials
H.Awata, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179, 647-666, 1996, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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 - 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, Refereed - 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 - Free Boson Representation of U_q(\widehat{sl}_3)
H.Awata, S.Odake and J.Shiraishi
LETTERS IN MATHEMATICAL PHYSICS, 30, 207-216, 1994, Refereed - Free Boson Realization of U_q(\widehat{sl}_N)
H.Awata, S.Odake and J.Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 162, 61-83, 1994, Refereed - 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, Refereed - 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, Refereed - 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, Refereed - 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 - Continuum Limit of Spin-1 Chain
T.Inami and S.Odake
Physical Review Letters, 70, 2016-2019, 1993, Refereed - Unitary Representations of $W$ Infinity Algebras
S.Odake
International Journal of Modern Physics, A7, 6339-6355, 1992, Refereed - W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry
S.Odake and T.Sano
Physics Letters, B258, 369-374, 1991, Refereed - 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 - Two Matrix Model and Minimal Unitary Model
S.Odake
Physics Letters, B269, 300-304, 1991, Refereed - Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
S.Odake
International Journal of Modern Physics, A5, 897-914, 1990, Refereed - c=3d Conformal Algebra with Extended Supersymmetry
S.Odake
Modern Physics Letters, A5, 561-580, 1990, Refereed - c=3d Algebra
S.Odake
Proceedings of the Workshop ``Topology, Field Theory and Superstring" KEK report, 89-22, 133-142, 1990 - Nonperturbative Analysis of Three Matrix Model
H.Kunitomo and S.Odake
Physics Letters, B247, 57-63, 1990, Refereed - Extension of N=2 Superconformal Algebra and Calabi-Yau Compactification
S.Odake
Modern Physics Letters, A4, 557-568, 1989, Refereed - Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
K.Kobayashi and S.Odake
Modern Physics Letters, A3, 773-781, 1988, Refereed - 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 - 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, Refereed - Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
A.Kato, Y.Matsuo and S.Odake
Physics Letters, B179, 241-246, 1986, Refereed
