Higher traces and characters of finite groups of Lie type

Abstract: I will give a brief overview of the theory of traces in higher categories and explain how this gives a new approach to the study of representation of finite groups of Lie type. Given an algebraic group $G$ over a finite field $\mathbb{F}_q$, I will explain how representations of $G(\mathbb{F}_q)$ arise as traces of categorical representations of $G$. Moreover, I will explain the higher categorical origin of Deligne-Lusztig representations and give a new conceptual computation of their characters which explains their regularity as a function of $q$. This is joint work with Gaitsgory and Varshavsky.

algebraic geometryrepresentation theory

Audience: researchers in the topic

Algebra and Geometry Seminar @ HKUST

Series comments: Algebra and Geometry seminar at the Hong Kong University of Science and Technology (HKUST).

If the talk is online/mixed mode, Zoom info is available on researchseminars.org in the talk details. But if you would also like to be added to the mailing list to get notifications for upcoming talks, please email agseminar@ust.hk.