Self-dual cuspidal and supercuspidal representations

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• Jeffrey Adler (American University)
• Tuesday 21 May 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jessica Fintzen.

According to the Harish-Chandra philosophy, cuspidal representations are the basic building blocks in the representation theory of finite reductive groups. Similarly for supercuspidal representations of p-adic groups. Self-dual representations play a special role in the study of parabolic induction. Thus, it is of interest to know whether self-dual (super)cuspidal representations exist. With a few exceptions involving some small fields, I will show precisely when a finite reductive group has irreducible cuspidal representations that are self-dual, of Deligne-Lusztig type, or both. Then I will look at implications for the existence of irreducible, self-dual supercuspidal representations of p-adic groups. This is joint work with Manish Mishra.

This talk is part of the Number Theory Seminar series.

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