Harish-Chandra modules over quantizations of nilpotent orbits.

Abstract: Let O be a nilpotent orbit in a semisimple Lie algebra over the complex numbers. Then it makes sense to talk about filtered quantizations of O, these are certain associative algebras that necessarily come with a preferred homomorphism from the universal enveloping algebra. Assume that the codimension of the boundary of O is at least 4, this is the case for all birationally rigid orbits (but six in the exceptional type), for example. In my talk I will explain a geometric classification of faithful irreducible Harish-Chandra modules over quantizations of O, concentrating on the case of canonical quantizations -- this gives rise to modules that could be called unipotent. The talk is based on a joint paper with Shilin Yu (in preparation).

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.