Infinite Dimensional Algebra Seminar

Friday, December 01, 2017 at 3:00pm to 5:00pm

2-361

Denis Gaitsgory (Harvard)

A chiral algebra responsible for quantum Langlands correspondence

In this talk we will report on a recent progress made by B.Feigin and the speaker of constructing a certain chiral algebra A that carries a Kac-Moody symmetry for a G and its Langlands dual G^L (at Langlands dual levels \kappa and \kappa^L). The localization of A on Bun_G\times Bun_{G^L} provides a kernel for the global quantum Langlands equivalence D_{\kappa}(Bun_G) -> D_{\kappa^L}(Bun_{G^L}). The category of chiral modules over A is a category acted on by the product of the loop groups G((t)) \times G^L((t)) and provides a kernel for the local quantum Langlands equivalence G((t))-Cat_{\kappa} -> G^L((t))-Cat_{\kappa^L}.

Event Type

Conferences/Seminars/Lectures

Events By Interest

Academic

Events By Audience

Public

Tags

harmonjo, midas_sem

Website

https://math.mit.edu/seminars/infdim/

Department
Department of Mathematics
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