R--groups, elliptic representations, and parameters for GSpin groups

2013/01/13 by Dubravka Ban, David Goldberg, Ban, Dubravka +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1301.2829

arxiv created 2013/01/13 · openalex publication_date 2013/01/13 · arxiv updated 2013/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study parabolically induced representations for GSpin_m(F) with F a p--adic field of characteristic zero. The Knapp-Stein R--groups are described and shown to be elementary two groups. We show the associated cocycle is trivial proving multiplicity one for induced representations. We classify the elliptic tempered spectrum. For GSpin_2n+1(F), we describe the Arthur (Endoscopic) R--group attached to Langlands parameters, and show these are isomorphic to the corresponding Knapp-Stein R--groups.

Citations

• On Certain L-Functions

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