Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2010): 22E50, 22E35

Retrieve articles in all journals with MSC (2010): 22E50, 22E35

Additional Information

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

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