Categorical Representation Theory and the Coarse Quotient

Tom Gannon (University of Texas)

30-Mar-2022, 20:00-21:00 (24 months ago)

Abstract: The main theorem of this talk will be that one can understand a "dense open" subset of DG categories with an action of a split reductive group G over a field of characteristic zero entirely in terms of its root datum. We will start by introducing the notion of a categorical representation of G and discuss some motivation. Then, we will discuss some of the main technical tools involved in making the statement of the main theorem precise, including discussion of the "coarse quotient" of the dual maximal Cartan by the affine Weyl group. We will also discuss how sheaves on this coarse quotient can be identified with bi-Whittaker sheaves on G, obtaining symmetric monoidal upgrade of a result of Ginzburg and Lonergan, and then give an outline of the proof of the main theorem. Time permitting, we will discuss some applications of these categorical representation theoretic ideas which prove a modified version of a conjecture of Ben-Zvi and Gunningham on the essential image of parabolic restriction.

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.

Organizers: André Lee Dixon*, Ju-Lee Kim, Roman Bezrukavnikov*
*contact for this listing

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