Doctor of Philosophy, The University of Tokyo

Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics, Elementary Particle Physics

Mathematical physics and fundamental theory of condensed matter physics, Mathematical physics

1986 - 1989, The University of Tokyo, Graduate School, Division of Science, Department of Physics

1984 - 1986, The University of Tokyo, Graduate School, Division of Science, Department of Physics

1980 - 1984, The University of Tokyo, Faculty of Science, Department of Physics

Some Difference Relations for Orthogonal Polynomials of a Continuous Variable in the Askey Scheme
Satoru Odake
Journal of Mathematical Analysis and Application, 560(2), 130625-130625, 2026, Refereed

Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes
Satoru Odake
Progress of Theoretical and Experimental Physics, 2025(4), Mar. 2025, Refereed

Type II multi-indexed little q-Jacobi and little q-Laguerre polynomials
Satoru Odake
Journal of Mathematical Physics, 66(1), Jan. 2025, 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

``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

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

Markov Chains Generated by Convolutions of Orthogonality Measures
S.Odake and R.Sasaki
Journal of Physics, 55(27), 275201, 2022, Refereed

Free Oscillator Realization of Laguerre Polynomial
S.Odake
Theoretical and Mathematical Physics, 210, 1-7, 2022, 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 VI : Meixner-Pollaczek and continuous Hahn types
S.Odake
Journal of Mathematical Physics, 61(5), 053505, 2020, 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

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

Orthogonal polynomials from Hermitian matrices. II
Satoru Odake; Ryu Sasaki
Journal of Mathematical Physics, 59(1), 013504, Jan. 2018, Refereed

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

New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics
Satoru Odake
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2017(5), 053A01, May 2017, Refereed

Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials
Satoru Odake; Ryu Sasaki
Journal of Physics A: Mathematical and Theoretical, 50(16), 165204, Mar. 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

Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
Satoru Odake; Ryu Sasaki
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 13, 020, 2017, Refereed

Recurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operators
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 57(11), 113503, Nov. 2016, Refereed

Recurrence relations of the multi-indexed orthogonal polynomials. III
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 57(2), 023514, Feb. 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

Solvable discrete quantum mechanics: q-orthogonal polynomials with vertical bar q vertical bar=1 and quantum dilogarithm
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 56(7), 073502, Jul. 2015, Refereed

Recurrence relations of the multi-indexed orthogonal polynomials. II
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 56(5), 053506, May 2015, Refereed

Casoratian identities for the Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF APPROXIMATION THEORY, 193, 184-209, May 2015, Refereed

Reflectionless potentials for difference Schrodinger equations
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 48(11), 115204, Mar. 2015, Refereed

Equivalences of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 55(1), 013502, Jan. 2014, Refereed

Non-polynomial extensions of solvable potentials à la Abraham-Moses
Satoru Odake; Ryu Sasaki
Journal of Mathematical Physics, 54(10), 102106, Oct. 2013, Refereed

Recurrence relations of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 54(8), 083506, Aug. 2013, Refereed

Krein-Adler transformations for shape-invariant potentials and pseudo virtual states
Satoru Odake; Ryu Sasaki
Journal of Physics A: Mathematical and Theoretical, 46(24), 245201, Jun. 2013, Refereed

Extensions of solvable potentials with finitely many discrete eigenstates
Satoru Odake; Ryu Sasaki
Journal of Physics A: Mathematical and Theoretical, 46(23), 235205, Jun. 2013, Refereed

Multi-indexed Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 46(4), 045204, Feb. 2013, Refereed

Multi-indexed (q-)Racah polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(38), 385201, Sep. 2012, Refereed

Discrete quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(35), 353001, Sep. 2011, Refereed

Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 702(2-3), 164-170, Aug. 2011, Refereed

Dual Christoffel Transformations
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 126(1), 1-34, Jul. 2011, Refereed

The Exceptional (X-l) (q)-Racah Polynomials
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 125(5), 851-870, May 2011, Refereed

A new family of shape invariantly deformed Darboux-Poschl-Teller potentials with continuous l
S. Odake; R. Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(19), 195203, May 2011, Refereed

Properties of the Exceptional (X-l) Laguerre and Jacobi Polynomial
Choon Lin Ho; Satoru Odake; Ryu Sasaki
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 7, 107, 2011, Refereed

Exceptional Askey-Wilson-type polynomials through Darboux-Crum transformations
S. Odake; R. Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 43(33), 335201, Aug. 2010, Refereed

Unified theory of exactly and quasiexactly solvable "discrete" quantum mechanics. I. Formalism
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 51(8), 083502, Aug. 2010, Refereed

Modification of Crum's Theorem for 'Discrete' Quantum Mechanics
Leonor Garcia-Gutierrez; Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 124(1), 1-26, Jul. 2010, Refereed

Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
S. Odake; R. Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 51(5), 053513, May 2010, Refereed

Another set of infinitely many exceptional (X-l) Laguerre polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 684(2-3), 173-176, Feb. 2010, Refereed

Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 682(1), 130-136, Nov. 2009, Refereed

Crum's Theorem for 'Discrete' Quantum Mechanics
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 122(5), 1067-1079, Nov. 2009, Refereed

Infinitely many shape invariant potentials and new orthogonal polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 679(4), 414-417, Aug. 2009, Refereed

Orthogonal polynomials from Hermitian matrices
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 49(5), 053503, May 2008, Refereed

Q-oscillator from the q-Hermite polynomial
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 663(1-2), 141-145, May 2008, Refereed

Exactly solvable 'discrete' quantum mechanics; Shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 119(4), 663-700, Apr. 2008

Multiparticle quasiexactly solvable difference equations
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(12), 122105, Dec. 2007, Refereed

Interpolation of SUSY quantum mechanics
Satoru Odake; Yamac Pehlivan; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 40(39), 11973-11986, Sep. 2007, Refereed

Exact Heisenberg operator solutions for multiparticle quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(8), 082106, Aug. 2007, Refereed

Unified theory of annihilation-creation operators for solvable ("discrete") quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 47(10), 102102 (33pages), Oct. 2006, Refereed

Exact solution in the Heisenberg picture and annihilation-creation operators
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 641(1), 112-117, Sep. 2006, Refereed

Calogero-Sutherland-Moser systems, Ruijsenaars-Schneider-van Diejen systems and orthogonal polynomials
S Odake; R Sasaki
PROGRESS OF THEORETICAL PHYSICS, 114(6), 1245-1260, Dec. 2005, Refereed

Equilibrium positions, shape invariance and Askey-Wilson polynomials
S Odake; R Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 46(6), 063513 (10pages), Jun. 2005, Refereed

Shape invariant potentials in "discrete quantum mechanics"
S Odake; R Sasaki
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 12, 507-521, Jan. 2005, Refereed

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

Equilibria of 'discrete' integrable systems and deformation of classical orthogonal polynomials
S Odake; G Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 37(49), 11841-11876, Dec. 2004, Refereed

Polynomials associated with equilibria of affine Toda-Sutherland systems
S Odake; R Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 37(47), 11401-11406, Nov. 2004, Refereed

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

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

Polynomials associated with equilibrium positions in Calogero-Moser systems
S Odake; R Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 35(39), 8283-8314, Oct. 2002, Refereed

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

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, 307-449, 2002

Free field construction for the ABF models in regime II
M Jimbo; H Konno; S Odake; Y Pugai; J Shiraishi
JOURNAL OF STATISTICAL PHYSICS, 102(3-4), 883-921, Feb. 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

Elliptic algebra Uqp(\hat{sl}2)
M.Jimbo; H.Konno; S.Odake; J.Shiraishi
Communications in Mathematical Physics, 199, 605-647, Dec. 1999, Refereed

Free field approach to the dilute A(L) models
Y Hara; M Jimbo; H Konno; S Odake; J Shiraishi
JOURNAL OF MATHEMATICAL PHYSICS, 40(8), 3791-3826, Aug. 1999, Refereed

Elliptic algebra U-q,U-p((sl)over-cap(2)): Drinfeld currents and vertex operators
M Jimbo; H Konno; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 199(3), 605-647, Jan. 1999, Refereed

Quasi-Hopf twistors for elliptic quantum groups
M Jimbo; H Konno; S Odake; J Shiraishi
TRANSFORMATION GROUPS, 4(4), 303-327, 1999, Refereed

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

Beyond the Conformal Field Theory : The Deformed Virasoro Algebra Opens A New Door
Awata Hidetoshi; Kubo Haruhiko; Morita Yoshifumi; Odake Satoru; Shiraishi Jun'ichi
日本物理学会誌, 53(3), 170-180, 1998

q-difference realization of U-q(sl(M/N)) and its application to free boson realization of U-q((sl)over-cap(2/1))
H Awata; S Odake; JI Shiraishi
LETTERS IN MATHEMATICAL PHYSICS, 42(3), 271-279, Nov. 1997, Refereed

Vertex operators of the q-Virasoro algebra; Defining relations, adjoint actions and four point functions
H Awata; H Kubo; Y Morita; S Odake; J Shiraishi
LETTERS IN MATHEMATICAL PHYSICS, 41(1), 65-78, Jul. 1997, Refereed

A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions
JI Shiraishi; H Kubo; H Awata; S Odake
LETTERS IN MATHEMATICAL PHYSICS, 38(1), 33-51, Sep. 1996, Refereed

Integral representations of the Macdonald symmetric polynomials
H Awata; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179(3), 647-666, Sep. 1996, Refereed

Quantum W-N algebras and Macdonald polynomials
H Awata; H Kubo; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179(2), 401-415, Aug. 1996, Refereed

Reflection K-matrices of the 19-vertex model and XXZ spin-1 chain with general boundary terms
T Inami; S Odake; YZ Zhang
NUCLEAR PHYSICS B, 470(3), 419-432, Jul. 1996, Refereed

SUPERSYMMETRIC EXTENSION OF THE SINE-GORDON THEORY WITH INTEGRABLE BOUNDARY INTERACTIONS
T INAMI; S ODAKE; YZ ZHANG
PHYSICS LETTERS B, 359(1-2), 118-124, Oct. 1995, Refereed

CHARACTER AND DETERMINANT FORMULAS OF QUASIFINITE REPRESENTATION OF THE W-1+INFINITY ALGEBRA
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 172(2), 377-400, Sep. 1995, Refereed

EXCITED-STATES OF THE CALOGERO-SUTHERLAND MODEL AND SINGULAR VECTORS OF THE W-N ALGEBRA
H AWATA; Y MATSUO; S ODAKE; J SHIRAISHI
NUCLEAR PHYSICS B, 449(1-2), 347-374, Aug. 1995, Refereed

QUASIFINITE HIGHEST WEIGHT MODULES OVER THE SUPER W-1+INFINITY ALGEBRA
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 170(1), 151-179, May 1995, Refereed

COLLECTIVE FIELD-THEORY, CALOGERO-SUTHERLAND MODEL AND GENERALIZED MATRIX MODELS
H AWATA; Y MATSUO; S ODAKE; J SHIRAISHI
PHYSICS LETTERS B, 347(1-2), 49-55, Mar. 1995, Refereed

SUBALGEBRAS OF W-1+INFINITY AND THEIR QUASIFINITE REPRESENTATIONS
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 28(1), 105-112, Jan. 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

REPRESENTATION-THEORY OF THE W-1+INFINITY ALGEBRA
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, (118), 343-373, 1995

REPRESENTATION-THEORY OF THE W-1+INFINITY ALGEBRA
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, 118(118), 343-373, 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

EIGENSYSTEM AND FULL CHARACTER FORMULA OF THE W-1+INFINITY ALGEBRA WITH C=1
H AWATA; M FUKUMA; S ODAKE; YH QUANO
LETTERS IN MATHEMATICAL PHYSICS, 31(4), 289-298, Aug. 1994, Refereed

DETERMINANT FORMULAS OF QUASI-FINITE REPRESENTATION OF W1+INFINITY ALGEBRA AT LOWER LEVELS
H AWATA; M FUKUMA; Y MATSUO; S ODAKE
PHYSICS LETTERS B, 332(3-4), 336-344, Jul. 1994, Refereed

FREE BOSON REALIZATION OF UQ(SLN)OVER-CAP
H AWATA; S ODAKE; J SHIRAISHI
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 162(1), 61-83, Apr. 1994, Refereed

FREE BOSON REPRESENTATION OF U(Q)((SL)OVER-CAP(3))
H AWATA; S ODAKE; J SHIRAISHI
LETTERS IN MATHEMATICAL PHYSICS, 30(3), 207-216, Mar. 1994, Refereed

HEISENBERG REALIZATION FOR UQ(SLN) ON THE FLAG MANIFOLD
H AWATA; M NOUMI; S ODAKE
LETTERS IN MATHEMATICAL PHYSICS, 30(1), 35-43, Jan. 1994, Refereed

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

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

Representation theory of W(1+infinity) algebra
Awata H; Fukuma M; Matsuo Y; Odake S
Group theoretical methods in physics. Proceedings, 40th Yamada Conference, 20th International Colloquium, Toyonaka, Japan, July 4-9, 1994, 335-338, 1994, Refereed

CONTINUUM-LIMIT OF SPIN-1 CHAIN
T INAMI; S ODAKE
PHYSICAL REVIEW LETTERS, 70(13), 2016-2019, Mar. 1993, Refereed

スピン１XXZ鎖の連続極限
小竹 悟
素粒子論研究, 87, 107-119, 1993

UNITARY REPRESENTATIONS OF W-INFINITY ALGEBRAS
S ODAKE
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 7(25), 6339-6355, Oct. 1992, Refereed

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

2-MATRIX MODEL AND MINIMAL UNITARY MODEL
S ODAKE
PHYSICS LETTERS B, 269(3-4), 300-304, Oct. 1991, Refereed

W1+-INFINITY AND SUPER-W-INFINITY ALGEBRAS WITH SU (N) SYMMETRY
S ODAKE; T SANO
PHYSICS LETTERS B, 258(3-4), 369-374, Apr. 1991, Refereed

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

NONPERTURBATIVE ANALYSIS OF THE 3 MATRIX MODEL
H KUNITOMO; S ODAKE
PHYSICS LETTERS B, 247(1), 57-63, Sep. 1990, Refereed

C = 3D CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY
S ODAKE
MODERN PHYSICS LETTERS A, 5(8), 561-580, Mar. 1990, Refereed

CHARACTER FORMULAS OF AN EXTENDED SUPERCONFORMAL ALGEBRA RELEVANT TO STRING COMPACTIFICATION
S ODAKE
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 5(5), 897-914, Mar. 1990, Refereed

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

EXTENSION OF N=2 SUPERCONFORMAL ALGEBRA AND CALABI-YAU COMPACTIFICATION
S ODAKE
MODERN PHYSICS LETTERS A, 4(6), 557-568, Mar. 1989, Refereed

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

OPERATOR PRODUCT EXPANSION COEFFICIENTS IN N = 1 SUPERCONFORMAL THEORY AND SLIGHTLY RELEVANT PERTUBATION
Y KITAZAWA; N ISHIBASHI; A KATO; K KOBAYASHI; Y MATSUO; S ODAKE
NUCLEAR PHYSICS B, 306(2), 425-444, Aug. 1988, Refereed

FERMIONIC CONSTRUCTION OF N=0,1,2 (SUPER) CONFORMAL ALGEBRAS
KI KOBAYASHI; S ODAKE
MODERN PHYSICS LETTERS A, 3(8), 773-781, Jul. 1988

FERMIONIC CONSTRUCTION OF N=0,1,2 (SUPER) CONFORMAL ALGEBRAS
KI KOBAYASHI; S ODAKE
MODERN PHYSICS LETTERS A, 3(8), 773-781, Jul. 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

Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
A.Kato, Y.Matsuo and S.Odake
Physics Letters, 75(5), E3-E5, 1987

Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
A.Kato; Y.Matsuo; S.Odake
PHYSICS LETTERS B, 179(3), 241-246, Oct. 1986, Refereed

Lepowsky-Wilson's Z Algebra and Deformed Virasoro Algebra
Hara Y.; Jimbo M.; Konno H.; Odake S.; Shiraishi J.
Meeting abstracts of the Physical Society of Japan, 55(2), 6 - 6, 10 Sep. 2000

RECENT DEVELOPMENTS IN STRING AND FIELD-THEORY - PREFACE
M KATO; H KUNITOMO; T NAKANISHI; S ODAKE; T ONOGI; M SAKAMOTO
PROGRESS OF THEORETICAL PHYSICS SUPPLEMENT, (110), R1 - R1, 1992

ストリング理論 第2巻
伊藤 克司,小竹 悟,松尾 泰, Joint work
シュプリンガー・フェアラーク東京, 2006

ストリング理論 第1巻
伊藤 克司,小竹 悟,松尾 泰, Joint work
シュプリンガー・フェアラーク東京, 2005

The Physical Society of Japan

Properties of new types of orthogonal polynomials and extensions of exactly solvable quantum mechanical systems
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C)
Shinshu University
01 Apr. 2019 - 31 Mar. 2023

Exactly Solvable Quantum Mechanics and New Orthogonal Polynomials
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C)
Shinshu University
01 Apr. 2013 - 31 Mar. 2017

Quantum symmetries and solvability
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C)
2011 - 2013

Integrable structure in field theory and string theory
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B)
Kyoto University
2006 - 2008

Space-Time Structure and Symmetry of Superstring Theory
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research on Priority Areas
The University of Tokyo
2001 - 2006

Massive Integrable Models and Infinite Dimensional Symmetries
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C)
Shinshu University
2000 - 2002

Algebraic Analysis of Quantum Integrable Systems
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B)
The University of Tokyo
2000 - 2001

Solvable Lattice Models and Elliptic Quantum Groups
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B)
KYOTO UNIVERSITY
1998 - 1999

量子変形されたビラソロ代数・W_N代数
科学研究費助成事業, 日本学術振興会, 奨励研究(A)
信州大学
1997 - 1998

ビラソロ代数・W_N代数の量子変形
科学研究費助成事業, 日本学術振興会, 重点領域研究
信州大学
1996 - 1996

W無限大代数の表現論とその応用
科学研究費助成事業, 日本学術振興会, 奨励研究(A)
信州大学
1995 - 1995

自由場表示によるq-頂点演算子の相関関数の研究
科学研究費助成事業, 日本学術振興会, 重点領域研究
信州大学
1995 - 1995

Quantum Field Theories in Low Dimensions and Their Application
Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science, Grant-in-Aid for Overseas Scientific Survey.
Kyoto University
1994 - 1994

自然界の根幹をなす素粒子論の究極の統一理論の候補である弦理論や、共形変換の下で不変な理論である共形場理論（弦理論や統計臨界系が含まれる）や、様々な可積分系を研究してきた。最近は解ける量子力学模型の研究を行っている。

素粒子理論・数理物理学（弦理論、共形場理論、無限次元代数、可積分系）