Standard Module Conjecture

2006/03/16 by Volker Heiermann, V. Heiermann, Heiermann, V. +3
Mathematics · #11F70 #22E50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F70 #msc:22E50

paper · pdf · doi:10.48550/arxiv.math/0603395

8 pages

arxiv created 2006/03/16 · openalex publication_date 2006/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a quasi-split p-adic group. Under the assumption that the local coefficients C_ψ defined with respect to ψ-generic tempered representations of standard Levi subgroups of G are regular in the negative Weyl chamber, we show that the standard module conjecture is true, which means that the Langlands quotient of a standard module is generic if and only if the standard module is irreducible.

Citations

• On Certain L-Functions

Related

• On the tempered L-function conjecture
• Genericity and contragredience in the local Langlands correspondence
• On submodules of standard modules
• On generic representations of quasi-split reductive groups over local fields of positive characteristic
• Local Langlands in families: The banal case