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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Self-dual cuspidal representations
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by Jeffrey D. Adler and Manish Mishra PDF
Represent. Theory 24 (2020), 210-228 Request permission

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
  • Email: jadler@american.edu
  • 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
  • Email: manish@iiserpune.ac.in
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 210-228
  • MSC (2000): Primary 20C33, 22E50
  • DOI: https://doi.org/10.1090/ert/541
  • MathSciNet review: 4105533