Speh representations are relatively discrete

Smith, Jerrod

doi:10.1090/ert/550

Speh representations are relatively discrete
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by Jerrod Manford Smith

Represent. Theory 24 (2020), 525-550

DOI: https://doi.org/10.1090/ert/550

Published electronically: October 27, 2020

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Abstract:

Let $F$ be a $p$-adic field of characteristic zero and odd residual characteristic. Let $\mathbf {Sp}_{2n}(F)$ denote the symplectic group defined over $F$, where $n\geq 2$. We prove that the Speh representations $\mathcal {U}(\delta ,2)$, where $\delta$ is a discrete series representation of $\mathbf {GL}_n(F)$, lie in the discrete spectrum of the $p$-adic symmetric space $\mathbf {Sp}_{2n}(F) \backslash \mathbf {GL}_{2n}(F)$.

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