R-groups and parameters

Dubravka Ban and David Goldberg

Vol. 255 (2012), No. 2, 281–303

DOI: 10.2140/pjm.2012.255.281

Abstract

Let G be a p-adic group, SO_2n+1, Sp_2n, O_2n or U_n. Let π be an irreducible discrete series representation of a Levi subgroup of G. We prove the conjecture that the Knapp–Stein R-group of π and the Arthur R-group of π are isomorphic. Several instances of the conjecture were established earlier: for archimedean groups by Shelstad; for principal series representations by Keys; for G = SO_2n+1 by Ban and Zhang; and for G = SO_n or Sp_2n in the case when π is supercuspidal, under an assumption on the parameter, by Goldberg.

Keywords

R-groups, reducibility of induced representations, classical groups

Mathematical Subject Classification 2010

Primary: 11F70, 22E35, 22E50

Milestones

Received: 25 February 2011

Revised: 30 August 2011

Accepted: 5 September 2011

Published: 10 April 2012