Generic unipotent standard modules

2009/09/29 by Dan Barbasch, Barbasch, Dan, Dan Ciubotaru +1
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:22E50

paper · pdf · doi:10.48550/arxiv.0909.5243

9 pages

openalex publication_date 2009/09/29 · arxiv created 2012/04/19 · arxiv updated 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Lusztig's geometric classification, we find the reducibility points of a standard module for the affine Hecke algebra, in the case when the inducing data is generic. This recovers the known result of Muic-Shahidi for representations of split p-adic groups with Iwahori-spherical Whittaker vectors. We also give a necessary (insufficient) condition for reducibility in the non-generic case.

Related

• On submodules of standard modules
• Hermitian duals and generic representations for affine Hecke algebras
• Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda
• On unitary unipotent representations of p-adic groups and affine Hecke algebras with unequal parameters
• Standard modules and intertwining operators for reductive p-adic groups