All Stories

  1. Type II multi-indexed little q-Jacobi and little q-Laguerre polynomials

    Article • Journal of Mathematical Physics, January 2025, American Institute of Physics

    Satoru Odake

  2. Discrete orthogonality relations for the multi-indexed orthogonal polynomials in discrete quantum mechanics with pure imaginary shifts

    Article • Journal of Mathematical Physics, May 2023, American Institute of Physics

    Satoru Odake

  3. Recurrence relations of the multi-indexed orthogonal polynomials. VI. Meixner–Pollaczek and continuous Hahn types

    Article • Journal of Mathematical Physics, May 2020, American Institute of Physics

    Satoru Odake

  4. Recurrence relations of the multi-indexed orthogonal polynomials V: Racah and q-Racah types

    Article • Journal of Mathematical Physics, February 2019, American Institute of Physics

    Satoru Odake

  5. Dual polynomials of the multi-indexed (q-)Racah orthogonal polynomials

    Article • Progress of Theoretical and Experimental Physics, July 2018, Oxford University Press (OUP)

    Satoru Odake

  6. Orthogonal polynomials from Hermitian matrices. II

    Article • Journal of Mathematical Physics, January 2018, American Institute of Physics

    Satoru Odake

  7. New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics

    Article • Progress of Theoretical and Experimental Physics, May 2017, Oxford University Press (OUP)

    Satoru Odake

  8. Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials

    Article • Symmetry Integrability and Geometry Methods and Applications, March 2017, SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

    Satoru Odake

  9. Multi-indexed Meixner and littleq-Jacobi (Laguerre) polynomials

    Article • Journal of Physics A Mathematical and Theoretical, March 2017, Institute of Physics Publishing

    Satoru Odake

  10. Recurrence relations of the multi-indexed orthogonal polynomials. IV. Closure relations and creation/annihilation operators

    Article • Journal of Mathematical Physics, November 2016, American Institute of Physics

    Satoru Odake

  11. Recurrence relations of the multi-indexed orthogonal polynomials. III

    Article • Journal of Mathematical Physics, February 2016, American Institute of Physics

    Satoru Odake

  12. Solvable discrete quantum mechanics: q-orthogonal polynomials with q=1 and quantum dilogarithm

    Article • Journal of Mathematical Physics, July 2015, American Institute of Physics

    Satoru Odake

  13. Casoratian identities for the Wilson and Askey–Wilson polynomials

    Article • Journal of Approximation Theory, May 2015, Elsevier

    Satoru Odake

  14. Recurrence relations of the multi-indexed orthogonal polynomials. II

    Article • Journal of Mathematical Physics, May 2015, American Institute of Physics

    Satoru Odake

  15. Reflectionless potentials for difference Schrödinger equations

    Article • Journal of Physics A Mathematical and Theoretical, February 2015, Institute of Physics Publishing

    Satoru Odake

  16. Equivalences of the multi-indexed orthogonal polynomials

    Article • Journal of Mathematical Physics, January 2014, American Institute of Physics

    Satoru Odake

  17. Non-polynomial extensions of solvable potentials à la Abraham-Moses

    Article • Journal of Mathematical Physics, October 2013, American Institute of Physics

    Satoru Odake

  18. Recurrence relations of the multi-indexed orthogonal polynomials

    Article • Journal of Mathematical Physics, August 2013, American Institute of Physics

    Satoru Odake

  19. Krein–Adler transformations for shape-invariant potentials and pseudo virtual states

    Article • Journal of Physics A Mathematical and Theoretical, May 2013, Institute of Physics Publishing

    Satoru Odake

  20. Extensions of solvable potentials with finitely many discrete eigenstates

    Article • Journal of Physics A Mathematical and Theoretical, May 2013, Institute of Physics Publishing

    Satoru Odake

  21. Preface

    Article • Progress of Theoretical Physics Supplement, May 2013, Oxford University Press (OUP)

    Satoru Odake

  22. Multi-indexed Wilson and Askey–Wilson polynomials

    Article • Journal of Physics A Mathematical and Theoretical, January 2013, Institute of Physics Publishing

    Satoru Odake

  23. Multi-indexed ( q -)Racah polynomials

    Article • Journal of Physics A Mathematical and Theoretical, August 2012, Institute of Physics Publishing

    Satoru Odake

  24. Properties of the Exceptional (Xl) Laguerre and Jacobi Polynomials

    Article • Symmetry Integrability and Geometry Methods and Applications, November 2011, SIGMA (Symmetry, Integrability and Geometry: Methods and Application)

    Satoru Odake

  25. Discrete quantum mechanics

    Article • Journal of Physics A Mathematical and Theoretical, August 2011, Institute of Physics Publishing

    Satoru Odake

  26. Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials

    Article • Physics Letters B, August 2011, Elsevier

    Satoru Odake

  27. Dual Christoffel Transformations

    Article • Progress of Theoretical Physics, July 2011, Oxford University Press (OUP)

    Satoru Odake

  28. The Exceptional (X ) (q)-Racah Polynomials

    Article • Progress of Theoretical Physics, May 2011, Oxford University Press (OUP)

    Satoru Odake

  29. A new family of shape invariantly deformed Darboux–Pöschl–Teller potentials with continuous ℓ

    Article • Journal of Physics A Mathematical and Theoretical, April 2011, Institute of Physics Publishing

    Satoru Odake

  30. Unified theory of exactly and quasiexactly solvable “discrete” quantum mechanics. I. Formalism

    Article • Journal of Mathematical Physics, August 2010, American Institute of Physics

    Satoru Odake

  31. Exceptional Askey–Wilson-type polynomials through Darboux–Crum transformations

    Article • Journal of Physics A Mathematical and Theoretical, July 2010, Institute of Physics Publishing

    Satoru Odake

  32. Modification of Crum's Theorem for 'Discrete' Quantum Mechanics

    Article • Progress of Theoretical Physics, July 2010, Oxford University Press (OUP)

    Satoru Odake

  33. Infinitely many shape-invariant potentials and cubic identities of the Laguerre and Jacobi polynomials

    Article • Journal of Mathematical Physics, May 2010, American Institute of Physics

    Satoru Odake

  34. Another set of infinitely many exceptional

    Article • Physics Letters B, February 2010, Elsevier

    Satoru Odake

  35. Crum's Theorem for 'Discrete' Quantum Mechanics

    Article • Progress of Theoretical Physics, November 2009, Oxford University Press (OUP)

    Satoru Odake

  36. Infinitely many shape invariant discrete quantum mechanical systems and new exceptional orthogonal polynomials related to the Wilson and Askey–Wilson polynomials

    Article • Physics Letters B, November 2009, Elsevier

    Satoru Odake

  37. Infinitely many shape invariant potentials and new orthogonal polynomials

    Article • Physics Letters B, August 2009, Elsevier

    Satoru Odake

  38. Orthogonal polynomials from Hermitian matrices

    Article • Journal of Mathematical Physics, May 2008, American Institute of Physics

    Satoru Odake

  39. q-oscillator from the q-Hermite polynomial

    Article • Physics Letters B, May 2008, Elsevier

    Satoru Odake

  40. Exactly Solvable 'Discrete' Quantum Mechanics; Shape Invariance, Heisenberg Solutions, Annihilation-Creation Operators and Coherent States

    Article • Progress of Theoretical Physics, April 2008, Oxford University Press (OUP)

    Satoru Odake

  41. Multiparticle quasiexactly solvable difference equations

    Article • Journal of Mathematical Physics, December 2007, American Institute of Physics

    Satoru Odake

  42. Interpolation of SUSY quantum mechanics

    Article • Journal of Physics A Mathematical and Theoretical, September 2007, Institute of Physics Publishing

    Satoru Odake

  43. Exact Heisenberg operator solutions for multiparticle quantum mechanics

    Article • Journal of Mathematical Physics, August 2007, American Institute of Physics

    Satoru Odake

  44. Unified theory of annihilation-creation operators for solvable (“discrete”) quantum mechanics

    Article • Journal of Mathematical Physics, October 2006, American Institute of Physics

    Satoru Odake

  45. Exact solution in the Heisenberg picture and annihilation–creation operators

    Article • Physics Letters B, September 2006, Elsevier

    Satoru Odake

  46. Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials

    Article • Progress of Theoretical Physics, December 2005, Oxford University Press (OUP)

    Satoru Odake

  47. Equilibrium positions, shape invariance and Askey–Wilson polynomials

    Article • Journal of Mathematical Physics, June 2005, American Institute of Physics

    Satoru Odake

  48. Shape Invariant Potentials in “Discrete Quantum Mechanics”

    Article • Journal of Nonlinear Mathematical Physics, January 2005, Taylor & Francis

    Satoru Odake

  49. Equilibria of ‘discrete’ integrable systems and deformation of classical orthogonal polynomials

    Article • Journal of Physics A General Physics, November 2004, Institute of Physics Publishing

    Satoru Odake

  50. Polynomials associated with equilibria of affine Toda–Sutherland systems

    Article • Journal of Physics A General Physics, November 2004, Institute of Physics Publishing

    Satoru Odake

  51. COMMENTS ON THE DEFORMED W N ALGEBRA

    Article • November 2002, World Scientific Pub Co Pte Lt

    Satoru Odake

  52. Polynomials associated with equilibrium positions in Calogero Moser systems

    Article • Journal of Physics A General Physics, September 2002, Institute of Physics Publishing

    Satoru Odake

  53. COMMENTS ON THE DEFORMED W N ALGEBRA

    Article • International Journal of Modern Physics B, June 2002, World Scientific Pub Co Pte Lt

    Satoru Odake

  54. Beyond CFT: Deformed Virasoro and Elliptic Algebras

    Article • January 2002, Springer Science + Business Media

    Satoru Odake

  55. On Lepowsky-Wilson’s

    Article • January 2002, American Mathematical Society (AMS)

    Satoru Odake

  56. Article • Journal of Statistical Physics, January 2001, Springer Science + Business Media

    Satoru Odake

  57. Quasi-Hopf twistors for elliptic quantum groups

    Article • Transformation Groups, December 1999, Springer Science + Business Media

    Satoru Odake

  58. Free field approach to the dilute AL models

    Article • Journal of Mathematical Physics, August 1999, American Institute of Physics

    Satoru Odake

  59. Elliptic Algebra $\Uqp(\slthbig)$ : Drinfeld Currents and Vertex Operators

    Article • Communications in Mathematical Physics, January 1999, Springer Science + Business Media

    Satoru Odake

  60. Article • Letters in Mathematical Physics, January 1997, Springer Science + Business Media

    Satoru Odake

  61. Article • Letters in Mathematical Physics, January 1997, Springer Science + Business Media

    Satoru Odake

  62. Integral representations of the Macdonald symmetric polynomials

    Article • Communications in Mathematical Physics, September 1996, Springer Science + Business Media

    Satoru Odake

  63. A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

    Article • Letters in Mathematical Physics, September 1996, Springer Science + Business Media

    Satoru Odake

  64. Quantum 401-1401-1401-1algebras and Macdonald polynomials

    Article • Communications in Mathematical Physics, August 1996, Springer Science + Business Media

    Satoru Odake

  65. Reflection K-matrices of the 19-vertex model and XXZ spin-1 chain with general boundary terms

    Article • Nuclear Physics B, July 1996, Elsevier

    Satoru Odake

  66. Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions

    Article • Physics Letters B, October 1995, Elsevier

    Satoru Odake

  67. Character and determinant formulae of quasifinite representation of theW 1+∞ algebra

    Article • Communications in Mathematical Physics, September 1995, Springer Science + Business Media

    Satoru Odake

  68. Excited states of the Calogero-Sutherland model and singular vectors of the WN algebra

    Article • Nuclear Physics B, August 1995, Elsevier

    Satoru Odake

  69. Quasifinite highest weight modules over the superW 1+∞algebra

    Article • Communications in Mathematical Physics, May 1995, Springer Science + Business Media

    Satoru Odake

  70. Collective field theory, Calogero-Sutherland model and generalized matrix models

    Article • Physics Letters B, March 1995, Elsevier

    Satoru Odake

  71. Subalgebras of W 1+ infinity and their quasifinite representations

    Article • Journal of Physics A General Physics, January 1995, Institute of Physics Publishing

    Satoru Odake

  72. Representation Theory of the W 1+∞ Algebra

    Article • Progress of Theoretical Physics Supplement, January 1995, Oxford University Press (OUP)

    Satoru Odake

  73. Eigensystem and full character formula of theW 1+? algebra withc = 1

    Article • Letters in Mathematical Physics, August 1994, Springer Science + Business Media

    Satoru Odake

  74. Determinant formulae of quasi-finite representation of W1+∞ algebra at lower levels

    Article • Physics Letters B, July 1994, Elsevier

    Satoru Odake

  75. Free boson realization of

    Article • Communications in Mathematical Physics, April 1994, Springer Science + Business Media

    Satoru Odake

  76. Free boson representation of $$U_q (\widehat{sl}_3 )$$

    Article • Letters in Mathematical Physics, March 1994, Springer Science + Business Media

    Satoru Odake

  77. Heisenberg realization for U q (sl n ) on the flag manifold

    Article • Letters in Mathematical Physics, January 1994, Springer Science + Business Media

    Satoru Odake

  78. Continuum limit of spin-1 chain

    Article • Physical Review Letters, March 1993, American Physical Society (APS)

    Satoru Odake

  79. UNITARY REPRESENTATIONS OF W INFINITY ALGEBRAS

    Article • International Journal of Modern Physics A, October 1992, World Scientific Pub Co Pte Lt

    Satoru Odake

  80. Two-matrix model and minimal unitary model

    Article • Physics Letters B, October 1991, Elsevier

    Satoru Odake

  81. W1+∞ and super-W∞ algebras with SU(N) symmetry

    Article • Physics Letters B, April 1991, Elsevier

    Satoru Odake

  82. Nonperturbative analysis of the three matrix model

    Article • Physics Letters B, September 1990, Elsevier

    Satoru Odake

  83. c=3d CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY

    Article • Modern Physics Letters A, March 1990, World Scientific Pub Co Pte Lt

    Satoru Odake

  84. CHARACTER FORMULAS OF AN EXTENDED SUPERCONFORMAL ALGEBRA RELEVANT TO STRING COMPACTIFICATION

    Article • International Journal of Modern Physics A, March 1990, World Scientific Pub Co Pte Lt

    Satoru Odake

  85. EXTENSION OF N = 2 SUPERCONFORMAL ALGEBRA AND CALABI-YAU COMPACTIFICATION

    Article • Modern Physics Letters A, March 1989, World Scientific Pub Co Pte Lt

    Satoru Odake

  86. Operator product expansion coefficients in N = 1 superconformal theory and slightly relevant perturbation

    Article • Nuclear Physics B, August 1988, Elsevier

    Satoru Odake

  87. FERMIONIC CONSTRUCTION OF N=0, 1, 2 (SUPER) CONFORMAL ALGEBRAS

    Article • Modern Physics Letters A, July 1988, World Scientific Pub Co Pte Lt

    Satoru Odake

  88. Modular invariance and two-loop bosonic string vacuum amplitude

    Article • Physics Letters B, October 1986, Elsevier

    Satoru Odake