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Representation Theory

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Speh representations are relatively discrete

Author: Jerrod Manford Smith
Journal: Represent. Theory 24 (2020), 525-550
MSC (2010): Primary 22E50; Secondary 22E35
Published electronically: October 27, 2020
MathSciNet review: 4166987
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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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Additional Information

Jerrod Manford Smith
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4
MR Author ID: 964846

Keywords: Relative discrete series, distinguished representation, symplectic group, Speh representation
Received by editor(s): August 3, 2018
Received by editor(s) in revised form: July 9, 2020
Published electronically: October 27, 2020
Article copyright: © Copyright 2020 American Mathematical Society