Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series

DOI10.1016/j.aim.2004.10.020zbMath1103.33010arXivmath/0407044OpenAlexW1990279876MaRDI QIDQ2369425

Bogdan Ion

Publication date: 9 May 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407044

zbMATH Keywords

semisimple groupsMacdonald polynomialsmatrix coefficientsprincipal serieszonal spherical functions

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Analysis on (p)-adic Lie groups (22E35) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) 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 (8)

Affine Hecke algebras via DAHA ⋮ Hecke modules from metaplectic ice ⋮ Spherical and Whittaker functions via DAHA. I. ⋮ Whittaker functions from motivic Chern classes ⋮ Whittaker functions and Demazure operators ⋮ Standard bases for affine parabolic modules and nonsymmetric Macdonald polynomials ⋮ Symmetric and nonsymmetric Koornwinder polynomials in the \(q \to 0\) limit ⋮ A combinatorial study of affine Schubert varieties in the affine Grassmannian

Cites Work

• Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup
• On the connection between Macdonald polynomials and Demazure characters
• Nonsymmetric Koornwinder polynomials and duality
• Nonsymmetric Macdonald polynomials and Demazure characters.
• Harmonic analysis for certain representations of graded Hecke algebras
• Reductive groups over a local field
• Affine Hecke Algebras and Their Graded Version
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