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, Not invited


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, Not invited


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, Not invited



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, Not invited


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, Not invited



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, Not invited



Recurrence relations of the multi-indexed orthogonal polynomials. III
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 57(2), 023514, Feb. 2016, Refereed, Not invited



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, Not invited



Recurrence relations of the multi-indexed orthogonal polynomials. II
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 56(5), 053506, May 2015, Refereed, Not invited



Casoratian identities for the Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF APPROXIMATION THEORY, 193, 184-209, May 2015, Refereed, Not invited



Reflectionless potentials for difference Schrodinger equations
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 48(11), 115204, Mar. 2015, Refereed, Not invited



Equivalences of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 55(1), 013502, Jan. 2014, Refereed, Not invited



Non-polynomial extensions of solvable potentials à la Abraham-Moses
Satoru Odake; Ryu Sasaki
Journal of Mathematical Physics, 54(10), 102106, Oct. 2013, Refereed, Not invited


Recurrence relations of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 54(8), 083506, Aug. 2013, Refereed, Not invited



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, Not invited


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, Not invited


Multi-indexed Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 46(4), 045204, Feb. 2013, Refereed, Not invited



Multi-indexed (q-)Racah polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(38), 385201, Sep. 2012, Refereed, Not invited



Discrete quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(35), 353001, Sep. 2011, Refereed, Not invited



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, Not invited



Dual Christoffel Transformations
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 126(1), 1-34, Jul. 2011, Refereed, Not invited



The Exceptional (X-l) (q)-Racah Polynomials
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 125(5), 851-870, May 2011, Refereed, Not invited



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, Not invited



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, Not invited



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, Not invited



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, Not invited



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, Not invited



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, Not invited



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, Not invited



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, Not invited



Crum's Theorem for 'Discrete' Quantum Mechanics
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 122(5), 1067-1079, Nov. 2009, Refereed, Not invited



Infinitely many shape invariant potentials and new orthogonal polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 679(4), 414-417, Aug. 2009, Refereed, Not invited



Orthogonal polynomials from Hermitian matrices
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 49(5), 053503, May 2008, Refereed, Not invited



Q-oscillator from the q-Hermite polynomial
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 663(1-2), 141-145, May 2008, Refereed, Not invited



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, Not invited



Multiparticle quasiexactly solvable difference equations
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(12), 122105, Dec. 2007, Refereed, Not invited



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, Not invited



Exact Heisenberg operator solutions for multiparticle quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(8), 082106, Aug. 2007, Refereed, Not invited



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, Not invited



Exact solution in the Heisenberg picture and annihilation-creation operators
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 641(1), 112-117, Sep. 2006, Refereed, Not invited



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, Not invited



Equilibrium positions, shape invariance and Askey-Wilson polynomials
S Odake; R Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 46(6), 063513 (10pages), Jun. 2005, Refereed, Not invited



Shape invariant potentials in "discrete quantum mechanics"
S Odake; R Sasaki
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 12, 507-521, Jan. 2005, Refereed, Not invited



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, Not invited


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, Not invited



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, Not invited



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, Not invited



Comments on the deformed W-N algebra
S Odake
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 16(14-15), 2055-2064, Jun. 2002, Refereed, Not invited



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, Not invited


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, Not invited



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, Not invited
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, Not invited


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, Not invited


Quasi-Hopf twistors for elliptic quantum groups
M Jimbo; H Konno; S Odake; J Shiraishi
TRANSFORMATION GROUPS, 4(4), 303-327, 1999, Refereed, Not invited


Quasi-Hopf twistors for elliptic quantum groups
M. Jimbo; S. Odake; H. Konno; J. Shiraishi
Transformation Groups, 4(4), 303-327, 1999, Not invited


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, Not invited


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, Not invited


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, Not invited


Integral representations of the Macdonald symmetric polynomials
H Awata; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179(3), 647-666, Sep. 1996, Refereed, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited

CONTINUUM-LIMIT OF SPIN-1 CHAIN
T INAMI; S ODAKE
PHYSICAL REVIEW LETTERS, 70(13), 2016-2019, Mar. 1993, Refereed, Not invited


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, Not invited


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, Not invited


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, Not invited


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, Not invited
NONPERTURBATIVE ANALYSIS OF THE 3 MATRIX MODEL
H KUNITOMO; S ODAKE
PHYSICS LETTERS B, 247(1), 57-63, Sep. 1990, Refereed, Not invited


C = 3D CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY
S ODAKE
MODERN PHYSICS LETTERS A, 5(8), 561-580, Mar. 1990, Refereed, Not invited


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, Not invited


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, Not invited


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, Not invited


FERMIONIC CONSTRUCTION OF N=0,1,2 (SUPER) CONFORMAL ALGEBRAS
KI KOBAYASHI; S ODAKE
MODERN PHYSICS LETTERS A, 3(8), 773-781, Jul. 1988, Not invited


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, Not invited


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, Not invited


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, Not invited


