Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

 
 

 

Self-dual cuspidal representations


Authors: Jeffrey D. Adler and Manish Mishra
Journal: Represent. Theory 24 (2020), 210-228
MSC (2000): Primary 20C33, 22E50
DOI: https://doi.org/10.1090/ert/541
Published electronically: June 2, 2020
MathSciNet review: 4105533
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

References

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 20C33, 22E50

Retrieve articles in all journals with MSC (2000): 20C33, 22E50


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

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