## Speh representations are relatively discrete

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- by Jerrod Manford Smith PDF
- Represent. Theory
**24**(2020), 525-550 Request permission

## 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 $\mathbf {Sp}_{2n}(F) \backslash \mathbf {GL}_{2n}(F)$.## References

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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
- Email: jerrod.smith@ucalgary.ca
- Received by editor(s): August 3, 2018
- Received by editor(s) in revised form: July 9, 2020
- Published electronically: October 27, 2020
- © Copyright 2020 American Mathematical Society
- Journal: Represent. Theory
**24**(2020), 525-550 - MSC (2010): Primary 22E50; Secondary 22E35
- DOI: https://doi.org/10.1090/ert/550
- MathSciNet review: 4166987