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Academic Organization	Academic Assembly　School of Science and Technology　Institute of Science	TEL
Education and Research Organization	Faculty of Science　Department of Science	FAX
Position	Professor	Mail Address
Address	Matsumoto 390-8621, Japan	Web site	http://azusa.shinshu-u.ac.jp/~odake/index.html

Profile

Assigned Class: Department of Material Science, Graduate School of Science and Technology (Master's Program)
Department of Materials Science and Engineering, Interdisciplinary Graduate School of Science and Technology (Doctor's Program)

Research Field: Elementary Particle Physics
Mathematical physics

Academic Societies: Academic Societies
The Physical Society of Japan

Academic Background: Graduate School
The University of Tokyo , (Department of Physics , Graduate School, Division of Science) , 1989
The University of Tokyo , (Department of Physics , Graduate School, Division of Science) , 1986

College
The University of Tokyo , (Faculty of Science) , 1984

Degree
Doctor of Philosophy , The University of Tokyo

Research

Books, Articles, etc.: Articles
Dual Polynomials of the Multi-Indexed (q-)Racah Orthogonal Polynomials
Progress of Theoretical and Experimental Physics,2018(7):073A02 2018
Author:S.Odake

Orthogonal polynomials from Hermitian matrices. II
Journal of Mathematical Physics,59(1):013504 2018
Author:S.Odake and R.Sasaki

Casoratian identities for the discrete orthogonal polynomials in discrete quantum mechanics with real shifts
Progress of Theoretical and Experimental Physics,2017(12):123A02 2017
Author:S.Odake

New Determinant Expressions of the Multi-indexed Orthogonal Polynomials in Discrete Quantum Mechanics
Progress of Theoretical and Experimental Physics,2017(5):053A01 2017
Author:S.Odake

Simplified Expressions of the Multi-indexed Laguerre and Jacobi Polynomials
SIGMA,13:020 2017
Author:S.Odake and R.Sasaki

Multi-indexed Meixner and Little q-Jacobi (Laguerre) Polynomials
Journal of Physics,50(16):165204 2016
Author:S.Odake and R.Sasaki

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials IV : closure relations and creation/annihilation operators
Journal of Mathematical Physics,57(11):113503 2016
Author:S.Odake

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : III
Journal of Mathematical Physics,57(2):023514 2016
Author:S.Odake

Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm
Journal of Mathematical Physics,56(7):073502 2015
Author:S.Odake and R.Sasaki

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials : II
Journal of Mathematical Physics,56(5):053506 2015
Author:S.Odake

Reflectionless Potentials for Difference Schr\"odinger Equations
Journal of Physics,A48(11):115204 2015
Author:S.Odake and R.Sasaki

Casoratian Identities for the Wilson and Askey-Wilson Polynomials
Journal of Approximation Theory,193:184-209 2015
Author:S.Odake and R.Sasaki

Equivalences of the multi-indexed orthogonal polynomials
Journal of Mathematical Physics,55:013502 2014
Author:S.Odake

Non-polynomial extensions of solvable potentials a la Abraham-Moses
Journal of Mathematical Physics,54:102106 2013
Author:S.Odake and R.Sasaki

Recurrence Relations of the Multi-Indexed Orthogonal Polynomials
Journal of Mathematical Physics,54:083506 2013
Author:S.Odake

Extensions of solvable potentials with finitely many discrete eigenstates
Journal of Physics,A46:235205 2013
Author:S.Odake and R.Sasaki

Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
Journal of Physics,A46:245201 2013
Author:S.Odake and R.Sasaki

Multi-indexed Wilson and Askey-Wilson Polynomials
Journal of Physics,A46:045204 2013
Author:S.Odake and R.Sasaki

Multi-indexed (q-)Racah Polynomials
Journal of Physics,A45:385201 2012
Author:S.Odake and R.Sasaki

Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
Physics Letters,B702:164 2011
Author:S.Odake and R.Sasaki

Discrete Quantum Mechanics
Journal of Physics,A44:353001 2011
Author:S.Odake and R.Sasaki

The Exceptional (X_{\ell}) (q)-Racah Polynomials
Progress of Theoretical Physics,125(5):851 2011
Author:S.Odake and R.Sasaki

Dual Christoffel transformations
Progress of Theoretical Physics,126:1 2011
Author:S.Odake and R.Sasaki

A new family of shape invariantly deformed Darboux-P\"oschl-Teller potentials with continuous \ell
Journal of Physics,A44:195203 2011
Author:S.Odake and R.Sasaki

Properties of the exceptional (X-l) Laguerre and Jacobi polynomials
SIGMA,7:107 2011
Author:C.-L.Ho, S.Odake and R.Sasaki

Exceptional Askey-Wilson type polynomials through Darboux-Crum transformations
Journal of Physics,A43:335201 2010
Author:S.Odake and R.Sasaki

Modification of Crum's Theorem for `Discrete' Quantum Mechanics
Progress of Theoretical Physics,124(1):1-26 2010
Author:L..Garcia-Gutierrez, S.Odake and R.Sasaki

Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
Journal of Mathematical Physics,51:083502 2010
Author:S.Odake and R.Sasaki

Another set of infinitely many exceptional ($X_{\ell}$) Laguerre polynomials
Physics Letters,B684:173-176 2010
Author:S.Odake and R.Sasaki

Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
Journal of Mathematical Physics,51:053513 2010
Author:S.Odake and R.Sasaki

Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
Physics Letters,B682:130 2009
Author:S.Odake and R.Sasaki

Infinitely many shape invariant potentials and new orthogonal polynomials
Physics Letters,B679:414 2009
Author:S.Odake and R.Sasaki

Crum's Theorem for `Discrete' Quantum Mechanics
Progress of Theoretical Physics,122(5):1067-1079 2009
Author:S.Odake and R.Sasaki

Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
Progress of Theoretical Physics,119(4):663-700 2008
Author:S.Odake and R.Sasaki

Orthogonal Polynomials from Hermitian Matrices
Journal of Mathematical Physics,49(5):053503 2008
Author:S.Odake and R.Sasaki

q-oscillator from the q-Hermite Polynomial
Physics Letters,B663(1-2):141-145 2008
Author:S.Odake and R.Sasaki

Multi-Particle Quasi Exactly Solvable Difference Equations
Journal of Mathematical Physics,48(12):122105 2007
Author:S.Odake and R.Sasaki

Interpolation of SUSY quantum mechanics
Journal of Physics,A40(39):11973-11986 2007
Author:S.Odake, Y.Pehlivan and R.Sasaki

Exact Heisenberg operator solutions for multi-particle quantum mechanics
Journal of Mathematical Physics,48(8):082106 2007
Author:S.Odake and R.Sasaki

Exact solution in the Heisenberg picture and annihilation-creation operators
Physics Letters,B641(1):112-117 2006
Author:S.Odake and R.Sasaki

Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
Journal of Mathematical Physics,47(10):102102 (33pages) 2006
Author:S.Odake and R.Sasaki

Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
Rokko Lectures in Mathematics (Kobe University) (Elliptic Integrable Systems, Eds. M.Noumi and K.Takasaki),18:85-110 2005
Author:S.Odake and R.Sasaki

Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
Progress of Theoretical Physics,114(6):1245-1260 2005
Author:S.Odake and R.Sasaki

Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
Journal of Mathematical Physics,46(6):063513 (10pages) 2005
Author:S.Odake and R.Sasaki

Shape Invariant Potentials in ``Discrete Quantum Mechanics"
Journal of Nonlinear Mathematical Physics,12 Supplement 1:507-521 2005
Author:S.Odake and R.Sasaki

Polynomials Associated with Equilibria of Affine Toda-Sutherland Systems
Journal of Physics,A37(47):11401-11406 2004
Author:S.Odake and R.Sasaki

Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
Journal of Physics,A37(49):11841-11876 2004
Author:S.Odake and R.Sasaki

Virasoro-type Symmetries in Solvable Models
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
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi

Quantum Deformation of the W_N Algebra
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
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi

Polynomials Associated with Equilibrium Positions in Calogero-Moser Systems
Journal of Physics,A35(39):8283-8314 2002
Author:S.Odake and R.Sasaki

Comments on the deformed W-N algebra
INTERNATIONAL JOURNAL OF MODERN PHYSICS B,16(14-15):2055-2064 2002
Author:S.Odake

On Lepowsky-Wilson's {\cal Z}-algebra
Contemporary Mathematics,297:143-149 2002
Author:Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi

Beyond CFT : Deformed Virasoro and Elliptic Algebras
`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
Author:S.Odake

Free Field Construction for the ABF Models in Regime II
Journal of Statistical Physics,102(3-4):883-921 2001
Author:M.Jimbo, H.Konno, S.Odake, Y.Pugai and J.Shiraishi

Quasi-Hopf twistors for elliptic quantum groups
`Yang-Baxter Systems, Nonlinear Models and Their Applications' edited by B.K. Chung, Q-Han Park and C.Rim,:173-182 2000
Author:S.Odake

Free Field Approach to the Dilute A_L Models
Journal of Mathematical Physics,40:3791-3826 1999
Author:Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi

Elliptic algebra U_{q,p}(\widehat{sl}_2) : Drinfeld currents and vertex operators
Communications in Mathematical Physics,199:605-647 1999
Author:M.Jimbo, H.Konno, S.Odake and J.Shiraishi

Quasi-Hopf twistors for elliptic quantum groups
Transformation Groups,4:303-327 1999
Author:M.Jimbo, H.Konno, S.Odake and J.Shiraishi

q-Difference Realization of U_q(sl(M|N)) and Its Application to Free Boson Realization of U_q(\widehat{sl}(2|1))
Letters in Mathematical Physics,42:271-279 1997
Author:H.Awata, S.Odake and J.Shiraishi

Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions
Letters in Mathematical Physics,41:65-78 1997
Author:H.Awata, H.Kubo, Y.Morita, S.Odake and J.Shiraishi

Reflection K-Matrices of the 19-Vertex Model and XXZ Spin-1 Chain with General Boundary Terms
Nuclear Physics,B470[FS]:419-432 1996
Author:T.Inami, S.Odake and Y-Z.Zhang

Quantum {\cal W}_N Algebras and Macdonald Polynomials
Communications in Mathematical Physics,179:401-416 1996
Author:H.Awata, H.Kubo, S.Odake and J.Shiraishi

A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
Letters in Mathematical Physics,38:33-51 1996
Author:J.Shiraishi, H.Kubo, H.Awata and S.Odake

Integral Representations of the Macdonald Symmetric Polynomials
Communications in Mathematical Physics,179:647-666 1996
Author:H.Awata, S.Odake and J.Shiraishi

Supersymmetric Extension of the Sine-Gordon Theory with Integrable Boundary Interaction
Physics Letters,B359:118-124 1995
Author:T.Inami, S.Odake and Y-Z.Zhang

A Note on Calogero-Sutherland Model, W_n Singular Vectors and Generalized Matrix Models
Soryushiron Kenkyu(Kyoto),91:A69-A75 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi

Excited States of Calogero-Sutherland Model and Singular Vectors of the W_N Algebra
Nuclear Physics,B449:347-374 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi

Collective Field Theory, Calogero--Sutherland Model and Generalized Matrix Models
Physics Letters,B347:49-55 1995
Author:H.Awata, Y.Matsuo, S.Odake and J.Shiraishi

Representation Theory of $W_{1+\infty}$ algebra
`Group Theoretical Methods in Physics' edited by A.Arima, T.Eguchi and N. Nakanishi,:335-338 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Representation Theory of The W_{1+\infty} Algebra
Progress of Theoretical Physics Proceedings Supplement,118:343-373 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations
Journal of Physics,A28:105-112 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Character and Determinant Formulae of Quasifinite Representation of the W_{1+\infty} Algebra
Communications in Mathematical Physics,172:377-400 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Quasifinite Highest Weight Modules over Super W_{1+\infty} Algebra
Communications in Mathematical Physics,170:151-179 1995
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
Physics Letters,B332:336-344 1994
Author:H.Awata, M.Fukuma, Y.Matsuo and S.Odake

Eigensystem and Full Character Formula of the {\cal W}_{1+\infty} Algebra with c=1
Letters in Mathematical Physics,31:289-298 1994
Author:H.Awata, M.Fukuma, S.Odake and Y.-H.Quano

Heisenberg realization for U_q(sl_n) on the flag manifold
Letters in Mathematical Physics,30:35-43 1994
Author:H.Awata, M.Noumi and S.Odake

Free Boson Realization of U_q(\widehat{sl}_N)
Communications in Mathematical Physics,162:61-83 1994
Author:H.Awata, S.Odake and J.Shiraishi

Free Boson Representation of U_q(\widehat{sl}_3)
Letters in Mathematical Physics,30:207-216 1994
Author:H.Awata, S.Odake and J.Shiraishi

Field Theory Limit of Spin-1 Chain
`Current Topics in Theoretical Physics' edited by Y.M.Cho,:113-124 1994
Author:T.Inami and S.Odake

Continuum Limit of Spin-1 Chain
Physical Review Letters,70:2016-2019 1993
Author:T.Inami and S.Odake

Unitary Representations of $W$ Infinity Algebras
International Journal of Modern Physics,A7:6339-6355 1992
Author:S.Odake

Two Matrix Model and Minimal Unitary Model
Physics Letters,B269:300-304 1991
Author:S.Odake

Comments on the $W_{1+\infty}$ and Super $W_{\infty}$ Algebras with $SU(N)$ Symmetry
KEK Proceedings,91-6:80-94 1991
Author:S.Odake and T.Sano

W_{1+\infty} and Super W_{\infty} Algebras with SU(N) Symmetry
Physics Letters,B258:369-374 1991
Author:S.Odake and T.Sano

Nonperturbative Analysis of Three Matrix Model
Physics Letters,B247:57-63 1990
Author:H.Kunitomo and S.Odake

c=3d Algebra
Proceedings of the Workshop ``Topology, Field Theory and Superstring" KEK report ,89-22:133-142 1990
Author:S.Odake

c=3d Conformal Algebra with Extended Supersymmetry
Modern Physics Letters,A5:561-580 1990
Author:S.Odake

Character Formulas of an Extended Superconformal Algebra Relevant to String Compactification
International Journal of Modern Physics,A5:897-914 1990
Author:S.Odake

Extension of N=2 Superconformal Algebra and Calabi-Yau Compactification
Modern Physics Letters,A4:557-568 1989
Author:S.Odake

Operator Product Expansion Coefficients in N=1 Superconformal Theory and Slightly Relevant Perturbation
Nuclear Physics,B306:425-444 1988
Author:Y.Kitazawa, N.Ishibashi, A.Kato, K.Kobayashi, Y.Matsuo and S.Odake

Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
Proceedings of 7th INS Winter Seminar on Superstrings, Composite Models and Anomaly Related Problems,:199-211 1988
Author:K.Kobayashi and S.Odake

Fermionic Construction of N=0,1,2 (Super)Conformal Algebras
Modern Physics Letters,A3:773-781 1988
Author:K.Kobayashi and S.Odake

Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
Physics Letters,B179:241-246 1986
Author:A.Kato, Y.Matsuo and S.Odake

Shinshu University Researcher Directory

ODAKE SATORU

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ODAKE　SATORU