Derived Chevalley isomorphisms

Abstract: For a reductive group G, the classical Chevalley isomorphism identifies conjugation-invariant functions on G with Weyl-invariant functions on its maximal torus. Berest-Ramadoss-Yeung have conjectured a derived upgrade of this statement, which predicts that the conjugation-invariant functions on the derived commuting variety of G identify with the Weyl-invariant functions on the derived commuting variety of its maximal torus. In joint work with Dennis Gaitsgory we deduce this conjecture for G = GL_n from investigations into derived aspects of the local Langlands correspondence. I’ll explain this story, assuming no background in derived algebraic geometry.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.