Iwahori-Hecke Algebras

Abstract

This article gives a fairly self-contained treatment of the basic facts about the Iwahori-Hecke algebra of a split p-adic group, including Bernstein's presentation, Macdonald's formula, the Casselman-Shalika formula, and the Lusztig-Kato formula.

25 pp. A fairly self-contained exposition of basic facts about Iwahori-Hecke algebras. Please send comments and corrections to [email protected]; reference added; slightly expanded introduction and other minor changes; submitted version

Cited by in corpus (14)

• The classification of irreducible admissible mod p representations of a p-adic GL_n
• A Satake isomorphism in characteristic p
• Introduction to Shimura varieties with bad reduction of parahoric type
• Banach-Hecke algebras and p-adic Galois Representations
• A tale of two Hecke algebras
• Fourier transform of the additive group in algebraically closed valued fields
• On the distribution of Satake parameters for Siegel modular forms
• Basic functions and unramified local L-factors for split groups
• Bernstein-Zelevinsky derivatives, branching rules and Hecke algebras
• An inverse Satake isomorphism in characteristic p
• Casselman's basis of Iwahori vectors and the Bruhat order
• Matrix Coefficients and Iwahori-Hecke Algebra Modules
• Nonsymmetric Macdonald polynomials and matrix coefficients for unramified principal series
• Generic pro-$p$ Hecke algebras