Selfdual cuspidal representations
Abstract
Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations that are selfdual, of DeligneLusztig type, or both. Finally, we outline some consequences for the existence of selfdual supercuspidal representations of reductive $p$adic groups.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 DOI:
 10.48550/arXiv.1903.02770
 arXiv:
 arXiv:1903.02770
 Bibcode:
 2019arXiv190302770A
 Keywords:

 Mathematics  Representation Theory;
 20C33;
 22E50
 EPrint:
 v2: Added some clarifications. v3: Deleted several extraneous words