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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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


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:
  • 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:
  • 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:
  • MathSciNet review: 4105533