Commuting difference operators with polynomial eigenfunctions

zbMath0838.33010arXivfunct-an/9306002MaRDI QIDQ4851973

Jan Felipe van Diejen

Publication date: 21 November 1995

Full work available at URL: https://arxiv.org/abs/funct-an/9306002

zbMATH Keywords

difference operatorsdifferential operatorsroot systemmultivariable polynomialsMacdonald polynomials

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Difference operators (39A70) Simple, semisimple, reductive (super)algebras (17B20) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (35)

Construction of eigenfunctions for the elliptic Ruijsenaars difference operators ⋮ Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term ⋮ Spin-Ruijsenaars, \(\mathsf{q}\)-deformed Haldane-Shastry and Macdonald polynomials ⋮ MacDonald-Koornwinder moments and the two-species exclusion process ⋮ Combinatorics of the two-species ASEP and Koornwinder moments ⋮ \(BC\)-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials ⋮ Kernel identities for van Diejen's \(q\)-difference operators and transformation formulas for multiple basic hypergeometric series ⋮ Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions ⋮ Quantum Lax pairs via Dunkl and Cherednik operators ⋮ Macdonald duality and the proof of the quantum Q-system conjecture ⋮ Scattering theory of the hyperbolic \(BC_n\) Sutherland and the rational \(BC_n\) Ruijsenaars-Schneider-Van Diejen models ⋮ Pieri formulas for Macdonald's spherical functions and polynomials ⋮ Multicomponent Calogero model of \(B_N\)-type confined in a harmonic potential ⋮ Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians ⋮ Multivariable \(q\)-Racah polynomials ⋮ Lectures on affine Hecke algebras and Macdonald’s conjectures ⋮ The Calogero-Sutherland model and polynomials with prescribed symmetry ⋮ Super-Macdonald polynomials: orthogonality and Hilbert space interpretation ⋮ Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an Appendix by S. Ruijsenaars) ⋮ Equivalence of two sets of Hamiltonians associated with the rational \(\operatorname{BC}_n\) Ruijsenaars-Schneider-van Diejen system ⋮ Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters ⋮ Branching formula for Macdonald-Koornwinder polynomials ⋮ The non-symmetric Wilson polynomials are the Bannai–Ito polynomials ⋮ Difference equations and Pieri formulas for \(G_2\) type Macdonald polynomials and integrability ⋮ Relativistic Calogero-Moser model as gauged WZW theory. ⋮ Rodrigues formulas for the non-symmetric multivariable polynomials associated with the \(\text{BC}_N\)-type root system ⋮ A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials ⋮ Bounded Littlewood identities ⋮ Properties of some families of hypergeometric orthogonal polynomials in several variables ⋮ Macdonald operators and quantum Q-systems for classical types ⋮ A duality of MacDonald-Koornwinder polynomials and its application to integral representations ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ Koornwinder polynomials and the \(XXZ\) spin chain ⋮ Macdonald polynomials and algebraic integrability ⋮ On a Poisson-Lie deformation of the \(\mathrm{BC}_{n}\) Sutherland system

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