Local unitary periods and relative discrete series

Jerrod Manford Smith

Vol. 297 (2018), No. 1, 225–256

DOI: 10.2140/pjm.2018.297.225

Abstract

Let $F$ be a $p$-adic field ($p\ne 2$), let $E$ be a quadratic Galois extension of $F$, and let $n\ge 2$. We construct representations in the discrete spectrum of the $p$-adic symmetric space $H\setminus G$, where $G=$GL${}_{2n}\left(E\right)$ and $H=$U${}_{E∕F}\left(F\right)$ is a quasisplit unitary group over $F$.

Keywords

relative discrete series, $p$-adic symmetric space, distinguished representation, unitary period, quasisplit unitary group

Mathematical Subject Classification 2010

Primary: 22E50

Secondary: 22E35

Milestones

Received: 24 November 2017

Revised: 20 June 2018

Accepted: 21 June 2018

Published: 7 October 2018