The Hecke algebra of a reductive p-adic group: a geometric conjecture

2005/02/11 by Anne‐Marie Aubert, Anne-Marie Aubert, Aubert, Anne-Marie +4
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.OA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0502234

45 pages

openalex publication_date 2005/02/11 · arxiv created 2005/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a conjecture for the ideals in the Bernstein decomposition of H(G). The conjecture says that each ideal is geometrically equivalent to an algebraic variety. Our conjecture is closely related to Lusztig's conjecture on the asymptotic Hecke algebra. We prove our conjecture for SL(2) and GL(n). We also prove part (1) of our conjecture for the Iwahori ideals of the groups PGL(n) and SO(5).

Related

• Recipes to compute the algebraic K-theory of Hecke algebras of reductive p-adic groups
• Algebraic K-theory of reductive p-adic groups
• On parameters of Hecke algebras for p-adic groups
• Remarks on the asymptotic Hecke algebra
• Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks