Commuting difference operators with polynomial eigenfunctions

Abstract

We present explicit generators of an algebra of commuting difference operators with trigonometric coefficients. The operators are simultaneously diagonalized by recently discovered q-polynomials (viz. Koornwinder's multivariable generalization of the Askey-Wilson polynomials). From the viewpoint of physics the algebra can be interpreted as consisting of the quantum integrals of a novel difference-type integrable sytem. This system generalizes the Calogero-Moser systems associated with non-exceptional root systems.

24 pp. (printing format: landscape), Latex (+ amssymbols.sty)

Cited by in corpus (30)

• Relativistic Calogero-Moser model as gauged WZW theory
• Self-dual Koornwinder-Macdonald polynomials
• The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry
• Properties of some families of hypergeometric orthogonal polynomials in several variables
• Limits of BC-type orthogonal polynomials as the number of variables goes to infinity
• Deformations of Calogero-Moser Systems
• The supersymmetric Ruijsenaars-Schneider model
• Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems
• Quantum Lax pairs via Dunkl and Cherednik operators
• Combinatorics of the two-species ASEP and Koornwinder moments
• Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials
• Koornwinder polynomials and the XXZ spin chain
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models
• A Unified Algebraic Approach to Few and Many-Body Correlated Systems
• Commuting difference operators arising from the elliptic C_2^{(1)}-face model
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• The Dn Ruijsenaars-Schneider model
• Creation operators for the Macdonald and Jack polynomials
• Branching Formula for Macdonald-Koornwinder Polynomials
• Structures in BC_N Ruijsenaars-Schneider models
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• On a Poisson-Lie deformation of the BC(n) Sutherland system
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• Branching Rules for Symmetric Hypergeometric Polynomials
• Dunkl and Cherednik operators
• Integrable many-body systems of Calogero-Ruijsenaars type
• Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• Plancherel formula for the quantum matrix ball - I