Deligne-Lusztig duality on the category of automorphic sheaves and categorical 2nd adjointness

Abstract: The Deligne-Lusztig duality in the title, which was conjectured by Drinfeld-Wang and Gaitsgory and proved by the speaker, relates the “miraculous duality” on the moduli stack G-torsors to certain parabolic induction/restriction functors. The (unramified) categorical 2nd adjointness, which was a folklore among the experts but proved and generalized by the speaker using nova methods, is a categorification of Bernstein’s famous 2nd adjointness. I will explain the relation between these two results, as well as the common ideas in their proofs: studying nearby cycles on certain geometric objects constructed from the Vinberg semi-group.

mathematical physicsalgebraic geometrycategory theoryrepresentation theory

Audience: researchers in the topic

UMass Amherst Representation theory seminar