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

Abstract

We provide an explicit construction of representations in the discrete spectrum of two $p$-adic symmetric spaces. We consider ${\mathbf{GL}}_n(F)\times {\mathbf{GL}}_n(F)\backslash {\mathbf{GL}}_{2n}(F)$ and ${\mathbf{GL}}_n(F)\backslash {\mathbf{GL}}_n(E)$, where $E$ is a quadratic Galois extension of a nonarchimedean local field $F$ of characteristic zero and odd residual characteristic. The proof of the main result involves an application of a symmetric space version of Casselman's Criterion for square integrability due to Kato and Takano.

31 pages, final version, author's draft, to appear in the Canadian Journal of Mathematics

Cited by in corpus (4)

• Local unitary periods and relative discrete series
• Speh representations are relatively discrete
• Linear periods and distinguished local parameters
• The support of closed orbit relative matrix coefficients