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Representation Theory

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Self-dual cuspidal representations

Authors: Jeffrey D. Adler and Manish Mishra
Journal: Represent. Theory 24 (2020), 210-228
MSC (2000): Primary 20C33, 22E50
Published electronically: June 2, 2020
MathSciNet review: 4105533
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Abstract: Let $G$ be a connected reductive group over a finite field $\mathfrak {f}$ of order $q$. When $q\leq 5$, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak {f})$ admits irreducible, cuspidal representations that are self-dual, of Deligne-Lusztig type, or both. Finally, we outline some consequences for the existence of self-dual supercuspidal representations of reductive $p$-adic groups.

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Additional Information

Jeffrey D. Adler
Affiliation: Department of Mathematics and Statistics, American University, 4400 Massachusetts Avenue NW, Washington, DC 20016-8050
MR Author ID: 604177

Manish Mishra
Affiliation: Department of Mathematics, Indian Institute for Science Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411 008, India
MR Author ID: 1097043
ORCID: 0000-0002-1471-0682

Keywords: Finite reductive group, $p$-adic group, cuspidal representation, supercuspidal representation, self-dual
Received by editor(s): August 20, 2019
Received by editor(s) in revised form: November 3, 2019
Published electronically: June 2, 2020
Additional Notes: The first-named author was partially supported by the American University College of Arts and Sciences Faculty Research Fund.
The second-named author was partially supported by SERB MATRICS and SERB ECR grants
Article copyright: © Copyright 2020 American Mathematical Society