## 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.## References

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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