\(R\)-groups and elliptic representations for \(SL_ n\)
type: Item
instance of: scholarly article
title: \(R\)-groups and elliptic representations for \(SL_ n\)
zbMATH Open document ID: 0855.22016
author: David Goldberg
published in: Pacific Journal of Mathematics
publication date: 1994-11-23T00:00:00Z
review text: The author continues his investigation of representations of classical \(p\)-adic groups that are parabolically induced from the discrete series. In this paper the group is \(\text{SL}_n (F)\) where \(F\) is a locally compact, non-discrete, non-archimedean field of characteristic zero. The reducibility and number of irreducible components is determined for any representation of \(\text{SL}_n (F)\) induced from a discrete series representation of a Levi subgroup. For this the theory of \(R\)-groups is used, and the \(R\)-groups are computed through restriction from \(\text{GL}_n (F)\), extending results of Gelbart and Knapp. The results are an explicit description of the elliptic tempered representations of \(\text{SL}_n (F)\) and, also, a description of those tempered representations that are not irreducibly induced from elliptic representations.
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 695065
zbMATH Keywords: induced representations
zbMATH Keywords: representations
zbMATH Keywords: \(p\)-adic groups
zbMATH Keywords: Levi subgroup
zbMATH Keywords: \(R\)-groups
zbMATH Keywords: tempered representations
zbMATH Keywords: elliptic representations
reviewed by: W. jun. Miller
MaRDI profile type: Publication
full work available at URL: pjm.1994.165.77
OpenAlex ID: W2042114516
DOI: 10.2140/PJM.1994.165.77
description: scientific article; zbMATH DE number 695065