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:05/08/2018

- 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)

- 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**

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

This system is developed with the collaboration of Shinshu University and Media Fusion Co., Ltd. (C) Shinshu University (C) Media Fusion Co., Ltd.