𝑞-Krawtchouk polynomials as spherical functions on the Hecke algebra of type 𝐵

DOI10.1090/S0002-9947-00-02588-5zbMath0957.33014arXivq-alg/9605040OpenAlexW1573370270MaRDI QIDQ4501126

H. T. Koelink

Publication date: 3 September 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9605040

zbMATH Keywords

Hecke algebrazonal spherical function\(q\)-Krawtchouk polynomial

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Harmonic analysis and spherical functions (43A90) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Introduction to Leonard pairs. ⋮ \(q\)-rotations and Krawtchouk polynomials ⋮ Tridiagonal pairs of \(q\)-Racah type ⋮ An algebraic interpretation of the \(q\)-Meixner polynomials ⋮ Spherical functions for Gelfand pairs of complex reflection groups ⋮ A discrete Fourier transform associated with the affine Hecke algebra ⋮ Leonard pairs from 24 points of view. ⋮ A tribute to Dennis Stanton ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS ⋮ Mehler-Heine type formulas for the Krawtchouk polynomials ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form

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