#### Vol. 297, No. 1, 2018

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Local unitary periods and relative discrete series

### Jerrod Manford Smith

Vol. 297 (2018), No. 1, 225–256
##### 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
Primary: 22E50
Secondary: 22E35