A duality of MacDonald-Koornwinder polynomials and its application to integral representations

DOI10.1215/S0012-7094-01-10723-0zbMath1012.33018MaRDI QIDQ1847821

Katsuhisa Mimachi

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

integral representationsMacdonald polynomialsduality formulaHeckman-Opdam's Jacobi polynomials of \(BC_n\) typeKoornwinder-Macdonald polynomials

Mathematics Subject Classification ID

Other hypergeometric functions and integrals in several variables (33C70) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (15)

Macdonald polynomials of type \(C_n\) with one-column diagrams and deformed Catalan numbers ⋮ Multivariate Jacobi polynomials and the Selberg integral. II ⋮ Refined Cauchy/Littlewood identities and six-vertex model partition functions. III. Deformed bosons ⋮ Multivariate Jacobi polynomials and the Selberg integral ⋮ Kernel identities for van Diejen's \(q\)-difference operators and transformation formulas for multiple basic hypergeometric series ⋮ Superconformal blocks in diverse dimensions and \textit{BC} symmetric functions ⋮ On the combinatorics of LLT polynomials in \(Sp_{2n}\) ⋮ Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions ⋮ Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP ⋮ Asymmetric simple exclusion process with open boundaries and Koornwinder polynomials ⋮ An asymptotic formula for the Koornwinder polynomials ⋮ An elliptic hypergeometric function approach to branching rules ⋮ Branching formula for Macdonald-Koornwinder polynomials ⋮ Bounded Littlewood identities ⋮ Source identities and kernel functions for the deformed Koornwinder-van Diejen models

Cites Work

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• Askey-Wilson polynomials by means of a \(q\)-Selberg type integral
• A generalization of Selberg’s beta integral
• Certain Hypergeometric Series Related to the Root System BC
• Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Jacobi Polynomials Associated with Selberg Integrals
• Properties of some families of hypergeometric orthogonal polynomials in several variables
• Commuting difference operators with polynomial eigenfunctions
• A new class of symmetric functions
• Self-dual Koornwinder-Macdonald polynomials

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