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arXiv · 1703.03450

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

Jerrod Manford Smith
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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.

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Jerrod Manford Smith. 2017-03-09. Relative discrete series representations for two quotients of $p$-adic $\mathbf{GL}_n$. https://doi.org/10.4153/cjm-2017-047-7

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