R-groups and elliptic representations for SL_n

David Goldberg

Vol. 165 (1994), No. 1, 77–92

DOI: 10.2140/pjm.1994.165.77

Abstract

We determine the reductibility and number of components of any representation of SL_n(F) which is parabolically induced from a discrete series representation. The R-groups are computed in terms of restriction from GL_n(F), extending the results of Gelbart and Knapp. This yields an explicit description of the elliptic tempered representations of SL_n(F). We also describe those tempered representations which are not irreducibly induced from elliptic representations.

Mathematical Subject Classification 2000

Primary: 22E55

Milestones

Received: 28 April 1992

Published: 1 September 1994