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), 2025年03月, 査読有り


Type II multi-indexed little
q-Jacobi and little
q-Laguerre polynomials
Satoru Odake
Journal of Mathematical Physics, 66(1), 2025年01月, 査読有り


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年, 査読有り


``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年, 査読有り


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年, 査読有り


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年, 査読有り


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


Free Oscillator Realization of Laguerre Polynomial
S.Odake
Theoretical and Mathematical Physics, 210, 1-7, 2022年, 査読有り


Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems
S.Odake
Journal of Physics, A53(36), 365202, 2020年, 査読有り


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年, 査読有り, 招待無し


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年, 査読有り


Recurrence Relations of the Multi-Indexed Orthogonal Polynomials V : Racah and q-Racah types
S.Odake
Journal of Mathematical Physics, 60(2), 023508, 2019年, 査読有り


Orthogonal polynomials from Hermitian matrices. II
Satoru Odake; Ryu Sasaki
Journal of Mathematical Physics, 59(1), 013504, 2018年01月, 査読有り, 招待無し


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


New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics
Satoru Odake
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS, 2017(5), 053A01, 2017年05月, 査読有り, 招待無し



Multi-indexed Meixner and little q-Jacobi (Laguerre) polynomials
Satoru Odake; Ryu Sasaki
Journal of Physics A: Mathematical and Theoretical, 50(16), 165204, 2017年03月, 査読有り, 招待無し


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年, 査読有り


Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials
Satoru Odake; Ryu Sasaki
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 13, 020, 2017年, 査読有り, 招待無し



Recurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operators
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 57(11), 113503, 2016年11月, 査読有り, 招待無し



Recurrence relations of the multi-indexed orthogonal polynomials. III
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 57(2), 023514, 2016年02月, 査読有り, 招待無し



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年, 査読有り

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, 2015年07月, 査読有り, 招待無し



Recurrence relations of the multi-indexed orthogonal polynomials. II
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 56(5), 053506, 2015年05月, 査読有り, 招待無し



Casoratian identities for the Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF APPROXIMATION THEORY, 193, 184-209, 2015年05月, 査読有り, 招待無し



Reflectionless potentials for difference Schrodinger equations
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 48(11), 115204, 2015年03月, 査読有り, 招待無し



Equivalences of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 55(1), 013502, 2014年01月, 査読有り, 招待無し



Non-polynomial extensions of solvable potentials à la Abraham-Moses
Satoru Odake; Ryu Sasaki
Journal of Mathematical Physics, 54(10), 102106, 2013年10月, 査読有り, 招待無し


Recurrence relations of the multi-indexed orthogonal polynomials
Satoru Odake
JOURNAL OF MATHEMATICAL PHYSICS, 54(8), 083506, 2013年08月, 査読有り, 招待無し



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, 2013年06月, 査読有り, 招待無し


Extensions of solvable potentials with finitely many discrete eigenstates
Satoru Odake; Ryu Sasaki
Journal of Physics A: Mathematical and Theoretical, 46(23), 235205, 2013年06月, 査読有り, 招待無し


Multi-indexed Wilson and Askey-Wilson polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 46(4), 045204, 2013年02月, 査読有り, 招待無し



Multi-indexed (q-)Racah polynomials
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45(38), 385201, 2012年09月, 査読有り, 招待無し



Discrete quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 44(35), 353001, 2011年09月, 査読有り, 招待無し



Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 702(2-3), 164-170, 2011年08月, 査読有り, 招待無し



Dual Christoffel Transformations
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 126(1), 1-34, 2011年07月, 査読有り, 招待無し



The Exceptional (X-l) (q)-Racah Polynomials
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 125(5), 851-870, 2011年05月, 査読有り, 招待無し



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, 2011年05月, 査読有り, 招待無し



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年, 査読有り, 招待無し



Exceptional Askey-Wilson-type polynomials through Darboux-Crum transformations
S. Odake; R. Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 43(33), 335201, 2010年08月, 査読有り, 招待無し



Unified theory of exactly and quasiexactly solvable "discrete" quantum mechanics. I. Formalism
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 51(8), 083502, 2010年08月, 査読有り, 招待無し



Modification of Crum's Theorem for 'Discrete' Quantum Mechanics
Leonor Garcia-Gutierrez; Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 124(1), 1-26, 2010年07月, 査読有り, 招待無し



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, 2010年05月, 査読有り, 招待無し



Another set of infinitely many exceptional (X-l) Laguerre polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 684(2-3), 173-176, 2010年02月, 査読有り, 招待無し



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, 2009年11月, 査読有り, 招待無し



Crum's Theorem for 'Discrete' Quantum Mechanics
Satoru Odake; Ryu Sasaki
PROGRESS OF THEORETICAL PHYSICS, 122(5), 1067-1079, 2009年11月, 査読有り, 招待無し



Infinitely many shape invariant potentials and new orthogonal polynomials
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 679(4), 414-417, 2009年08月, 査読有り, 招待無し



Orthogonal polynomials from Hermitian matrices
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 49(5), 053503, 2008年05月, 査読有り, 招待無し



Q-oscillator from the q-Hermite polynomial
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 663(1-2), 141-145, 2008年05月, 査読有り, 招待無し



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, 2008年04月, 招待無し



Multiparticle quasiexactly solvable difference equations
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(12), 122105, 2007年12月, 査読有り, 招待無し



Interpolation of SUSY quantum mechanics
Satoru Odake; Yamac Pehlivan; Ryu Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 40(39), 11973-11986, 2007年09月, 査読有り, 招待無し



Exact Heisenberg operator solutions for multiparticle quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 48(8), 082106, 2007年08月, 査読有り, 招待無し



Unified theory of annihilation-creation operators for solvable ("discrete") quantum mechanics
Satoru Odake; Ryu Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 47(10), 102102 (33pages), 2006年10月, 査読有り, 招待無し



Exact solution in the Heisenberg picture and annihilation-creation operators
Satoru Odake; Ryu Sasaki
PHYSICS LETTERS B, 641(1), 112-117, 2006年09月, 査読有り, 招待無し



Calogero-Sutherland-Moser systems, Ruijsenaars-Schneider-van Diejen systems and orthogonal polynomials
S Odake; R Sasaki
PROGRESS OF THEORETICAL PHYSICS, 114(6), 1245-1260, 2005年12月, 査読有り, 招待無し



Equilibrium positions, shape invariance and Askey-Wilson polynomials
S Odake; R Sasaki
JOURNAL OF MATHEMATICAL PHYSICS, 46(6), 063513 (10pages), 2005年06月, 査読有り, 招待無し



Shape invariant potentials in "discrete quantum mechanics"
S Odake; R Sasaki
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 12, 507-521, 2005年01月, 査読有り, 招待無し



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年, 査読有り, 招待無し


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, 2004年12月, 査読有り, 招待無し



Polynomials associated with equilibria of affine Toda-Sutherland systems
S Odake; R Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 37(47), 11401-11406, 2004年11月, 査読有り, 招待無し



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年
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年
Polynomials associated with equilibrium positions in Calogero-Moser systems
S Odake; R Sasaki
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 35(39), 8283-8314, 2002年10月, 査読有り, 招待無し



Comments on the deformed W-N algebra
S Odake
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 16(14-15), 2055-2064, 2002年06月, 査読有り, 招待無し



On Lepowsky-Wilson's {\cal Z}-algebra
Y.Hara, M.Jimbo, H.Konno, S.Odake and J.Shiraishi
Contemporary Mathematics, 297, 143-149, 2002年, 査読有り
Beyond CFT: Deformed Virasoro and elliptic algebras
S Odake
THEORETICAL PHYSICS AT THE END OF THE TWENTIETH CENTURY, 307-449, 2002年, 招待無し


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, 2001年02月, 査読有り, 招待無し



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年
Elliptic algebra Uqp(\hat{sl}2)
M.Jimbo; H.Konno; S.Odake; J.Shiraishi
Communications in Mathematical Physics, 199, 605-647, 1999年12月, 査読有り, 招待無し
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, 1999年08月, 査読有り, 招待無し


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, 1999年01月, 査読有り, 招待無し


Quasi-Hopf twistors for elliptic quantum groups
M Jimbo; H Konno; S Odake; J Shiraishi
TRANSFORMATION GROUPS, 4(4), 303-327, 1999年, 査読有り, 招待無し


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


共形場理論を越えて -- 変形 Virasoro 代数が開く扉 --
粟田 英資, 久保 晴信, 守田 佳史, 小竹 悟, 白石 潤一
日本物理学会誌, 53(3), 170-180, 1998年

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, 1997年11月, 査読有り, 招待無し


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, 1997年07月, 査読有り, 招待無し


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, 1996年09月, 査読有り, 招待無し


Integral representations of the Macdonald symmetric polynomials
H Awata; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179(3), 647-666, 1996年09月, 査読有り, 招待無し


Quantum W-N algebras and Macdonald polynomials
H Awata; H Kubo; S Odake; J Shiraishi
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 179(2), 401-415, 1996年08月, 査読有り, 招待無し


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, 1996年07月, 査読有り, 招待無し


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, 1995年10月, 査読有り, 招待無し


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, 1995年09月, 査読有り, 招待無し


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, 1995年08月, 査読有り, 招待無し


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, 1995年05月, 査読有り, 招待無し


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, 1995年03月, 査読有り, 招待無し


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, 1995年01月, 査読有り, 招待無し


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年
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年, 招待無し


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年, 査読有り, 招待無し


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年, 査読有り
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, 1994年08月, 査読有り, 招待無し


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, 1994年07月, 査読有り, 招待無し


FREE BOSON REALIZATION OF UQ(SLN)OVER-CAP
H AWATA; S ODAKE; J SHIRAISHI
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 162(1), 61-83, 1994年04月, 査読有り, 招待無し


FREE BOSON REPRESENTATION OF U(Q)((SL)OVER-CAP(3))
H AWATA; S ODAKE; J SHIRAISHI
LETTERS IN MATHEMATICAL PHYSICS, 30(3), 207-216, 1994年03月, 査読有り, 招待無し


HEISENBERG REALIZATION FOR UQ(SLN) ON THE FLAG MANIFOLD
H AWATA; M NOUMI; S ODAKE
LETTERS IN MATHEMATICAL PHYSICS, 30(1), 35-43, 1994年01月, 査読有り, 招待無し


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年
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年
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年, 査読有り, 招待無し

CONTINUUM-LIMIT OF SPIN-1 CHAIN
T INAMI; S ODAKE
PHYSICAL REVIEW LETTERS, 70(13), 2016-2019, 1993年03月, 査読有り, 招待無し


スピン1XXZ鎖の連続極限
小竹 悟
素粒子論研究, 87, 107-119, 1993年
UNITARY REPRESENTATIONS OF W-INFINITY ALGEBRAS
S ODAKE
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 7(25), 6339-6355, 1992年10月, 査読有り, 招待無し


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年
2-MATRIX MODEL AND MINIMAL UNITARY MODEL
S ODAKE
PHYSICS LETTERS B, 269(3-4), 300-304, 1991年10月, 査読有り, 招待無し


W1+-INFINITY AND SUPER-W-INFINITY ALGEBRAS WITH SU (N) SYMMETRY
S ODAKE; T SANO
PHYSICS LETTERS B, 258(3-4), 369-374, 1991年04月, 査読有り, 招待無し


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年, 招待無し
NONPERTURBATIVE ANALYSIS OF THE 3 MATRIX MODEL
H KUNITOMO; S ODAKE
PHYSICS LETTERS B, 247(1), 57-63, 1990年09月, 査読有り, 招待無し


C = 3D CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY
S ODAKE
MODERN PHYSICS LETTERS A, 5(8), 561-580, 1990年03月, 査読有り, 招待無し


CHARACTER FORMULAS OF AN EXTENDED SUPERCONFORMAL ALGEBRA RELEVANT TO STRING COMPACTIFICATION
S ODAKE
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 5(5), 897-914, 1990年03月, 査読有り, 招待無し


c=3d Algebra
S.Odake
Proceedings of theWorkshop ``Topology, Field Theory and Superstring" KEK report, 89-22, 133-142, 1990年
EXTENSION OF N=2 SUPERCONFORMAL ALGEBRA AND CALABI-YAU COMPACTIFICATION
S ODAKE
MODERN PHYSICS LETTERS A, 4(6), 557-568, 1989年03月, 査読有り, 招待無し


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年
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, 1988年08月, 査読有り, 招待無し


FERMIONIC CONSTRUCTION OF N=0,1,2 (SUPER) CONFORMAL ALGEBRAS
KI KOBAYASHI; S ODAKE
MODERN PHYSICS LETTERS A, 3(8), 773-781, 1988年07月, 招待無し


FERMIONIC CONSTRUCTION OF N=0,1,2 (SUPER) CONFORMAL ALGEBRAS
KI KOBAYASHI; S ODAKE
MODERN PHYSICS LETTERS A, 3(8), 773-781, 1988年07月, 査読有り, 招待無し


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年
Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
加藤 晃史; 松尾 泰; 小竹 悟
素粒子論研究, 75(5), E3-E5, 1987年, 招待無し


Modular Invariance and Two-Loop Bosonic String Vacuum Amplitude
A.Kato, Y.Matsuo and S.Odake
Physics Letters, 179(3), 241-246, 1986年10月, 査読有り, 招待無し


