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 |

Modified:09/04/2019

- Assigned Class
- Graduate School of Science and Technology, Department of Science, Science Division, Physics Unit (Master's Program)

Graduate School of Medicine, Science and Technology, Department of Science and Technology, Materials Science and Engineering, Matter and Spacetime Sciences (Doctor's Program)

- 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

- Books, Articles, etc.
**Articles**

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

Journal of Mathematical Physics,60(2):023508 2019

Author:S.Odake

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

解ける量子力学模型と直交多項式

日本物理学会誌,71(3):156-163 2016

Author:小竹 悟

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

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