On representations of ${\rm GL}_{2n}(F)$ with a symplectic period

Arnab Mitra

Vol. 268 (2014), No. 2, 435–463

DOI: 10.2140/pjm.2014.268.435

Abstract

Given a nonarchimedean local field $F$, we classify the irreducible admissible representations of ${GL}_4\left(F\right)$ and ${GL}_6\left(F\right)$ that bear a nontrivial linear form invariant under the groups $S{p}_2\left(F\right)$ and $S{p}_3\left(F\right)$, respectively. We propose a few conjectures for the case of ${GL}_{2n}\left(F\right)$, $n>3$.

Keywords

admissible, symplectic period

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 11F70

Milestones

Received: 7 March 2012

Revised: 21 October 2012

Accepted: 29 October 2012

Published: 21 June 2014