MIT Lie Groups Seminar

Wednesday, April 24, 2024 at 4:00pm to 6:00pm

Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139

Speaker:  Charlotte Chan (University of Michigan)   

Title:  Generic character sheaves on parahoric subgroups

Abstract:  Lusztig's theory of character sheaves for connected reductive groups is one of the most important developments in representation theory in the last few decades. I will give a brief overview of this theory and explain the need, from the perspective of the representation theory of p-adic groups, of a theory of character sheaves on jet schemes. Recently, R. Bezrukavnikov and I have developed the "generic" part of this desired theory. In the simplest nontrivial case, this resolves a conjecture of Lusztig and produces perverse sheaves on jet schemes compatible with parahoric Deligne--Lusztig induction. This talk is intended to describe what we know about these generic character sheaves, especially within the context of the Langlands program.

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