On Langlands quotients of the generalized principal series isomorphic to their Aubert duals

Ivan Matić

Vol. 289 (2017), No. 2, 395–415

DOI: 10.2140/pjm.2017.289.395

Abstract

We determine under which conditions is the Langlands quotient of an induced representation of the form $\delta ⋊\sigma$, where $\delta$ is an irreducible essentially square-integrable representation of a general linear group and $\sigma$ is a discrete series representation of the classical $p$-adic group, isomorphic to its Aubert dual.

Keywords

discrete series, classical $p$-adic groups, Aubert involution

Mathematical Subject Classification 2010

Primary: 22E35

Secondary: 11F70, 22E50

Milestones

Received: 21 October 2016

Revised: 10 February 2017

Accepted: 28 February 2017

Published: 19 June 2017