Supercuspidal representations of GL(n) distinguished by a unitary subgroup

Jeffrey Hakim and Zhengyu Mao

Vol. 185 (1998), No. 1, 149–162

DOI: 10.2140/pjm.1998.185.149

Abstract

When E∕F is a quadratic extension of p-adic fields, with p≠2, and H′ is a unitary similitude group in GL(n,E), it is shown that for every irreducible supercuspidal representation π of GL(n,E) of lowest level the space of H′-invariant linear forms has dimension at most one. The analogous fact for the corresponding unitary group H also holds, so long as n is odd or E∕F is ramified. When n is even and E∕F is unramified, the space of H-invariant linear forms on the space of π may have dimension two.

Milestones

Received: 23 January 1997

Revised: 15 May 1997

Published: 1 September 1998