Kernel identities for van Diejen's \(q\)-difference operators and transformation formulas for multiple basic hypergeometric series

DOI10.1007/s11139-012-9449-8zbMath1279.33026arXiv1112.4230OpenAlexW2963936858MaRDI QIDQ386501

Yasuho Masuda

Publication date: 9 December 2013

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.4230

zbMATH Keywords

affine Hecke algebrasKoornwinder polynomialsmultiple basic hypergeometric seriesvan Diejen's \(q\)-difference operators

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Basic hypergeometric functions associated with root systems (33D67)

Related Items (2)

Duality transformation formulas for multiple elliptic hypergeometric series of type \(BC\) ⋮ An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type \(A\)

Cites Work

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• An (inverse) Pieri formula for Macdonald polynomials of type \(C\)
• Kernel functions for difference operators of Ruijsenaars type and their applications
• Balanced \(_ 3\phi_ 2\) summation theorems for \(U(n)\) basic hypergeometric series
• An integral representation of eigenfunctions for Macdonald's \(q\)-difference operators
• Karlsson--Minton type hypergeometric functions on the root system \(C_{n}\)
• Nonsymmetric Koornwinder polynomials and duality
• Double affine Hecke algebras and Macdonald's conjectures
• A duality of MacDonald-Koornwinder polynomials and its application to integral representations
• Euler transformation formula for multiple basic hypergeometric series of type \(A\) and some applications
• Affine Hecke algebras and raising operators for Macdonald polynomials
• Integrability of difference Calogero–Moser systems
• Commuting difference operators with polynomial eigenfunctions
• Self-dual Koornwinder-Macdonald polynomials

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