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

Abstract

We study parabolically induced representations for $GSpi{n}_m(F)$ 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 $GSpi{n}_{2n+1}(F)$, we describe the Arthur (Endoscopic) $R$--group attached to Langlands parameters, and show these are isomorphic to the corresponding Knapp-Stein $R$--groups.

References in corpus (1)

• Dual R-groups of the inner forms of SL(N)