Local unitary periods and relative discrete series

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 $H\backslash G$, where $G={\mathbf{GL}}_{2n}(E)$ and $H={\mathbf{U}}_{E/F}(F)$ is a quasi-split unitary group over $F$.

30 pages, to appear in the Pacific Journal of Mathematics. In version 2: Section 5.4 added; Proposition 5.12 improved; some results in Section 5.3 renumbered; bibliography updated; several typos corrected. This work extends the results of arXiv:1703.03450 via similar methods

References in corpus (1)

• Relative discrete series representations for two quotients of $p$-adic ${\mathbf{GL}}_n$

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• The support of closed orbit relative matrix coefficients