論文 New Finite Type Multi-Indexed Orthogonal Polynomials Obtained From State-Adding Darboux Transformations Progress of Theoretical and Experimental Physics,2023(7):073A01 2023 Author:S.Odake
Discrete Orthogonality Relations for the Multi-Indexed Orthogonal Polynomials in Discrete Quantum Mechanics with Pure Imaginary Shifts Journal of Mathematical Physics,64(5):53503 2023 Author:S.Odake
Markov Chains Generated by Convolutions of Orthogonality Measures Journal of Physics,55(27):275201 2022 Author:S.Odake and R.Sasaki
Free Oscillator Realization of Laguerre Polynomial Theoretical and Mathematical Physics,210:1-7 2022 Author:S.Odake
Wronskian/Casoratian Identities and their Application to Quantum Mechanical Systems Journal of Physics,A53(36):365202 2020 Author:S.Odake
Recurrence Relations of the Multi-Indexed Orthogonal Polynomials VI : Meixner-Pollaczek and continuous Hahn types Journal of Mathematical Physics,61(5):053505 2020 Author:S.Odake
Exactly Solvable Discrete Quantum Mechanical Systems and Multi-indexed Orthogonal Polynomials of the Continuous Hahn and Meixner-Pollaczek Types Progress of Theoretical and Experimental Physics,2019(12):123A01 2019 Author:S.Odake
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
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
場の理論的方法によるスピン鎖 物性研究,61:648-653 1994 Author:小竹 悟
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
スピン１XXZ鎖の連続極限 素粒子論研究,87:107-119 1993 Author:小竹 悟
Continuum Limit of Spin-1 Chain Physical Review Letters,70:2016-2019 1993 Author:T.Inami and S.Odake
W 無限大代数のユニタリ表現 素粒子論研究,85:237-254 1992 Author:小竹 悟
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
超共形代数とその拡張について 素粒子論研究,78:201-260 1989 Author:小竹 悟
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
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