Self-dual cuspidal representations

Adler, Jeffrey; Mishra, Manish

doi:10.1090/ert/541

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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