Geometric Representation Theory Seminar

Monday, October 22, 2018 at 5:30pm to 6:30pm

2-449, 2-449

Dennis Gaitsgory (Harvard)

An extension of the Kazhdan-Lusztig equivalence to category O

The Kazhdan-Lusztig equivalence says that for a negative level -\kappa, the category KL(G,-\kappa) of G(O)-integrable modules over the Kac-Moody algebra \hat{g} at level -\kappa is equivalent to the category of finite-dimensional modules over Lusztig's quantum group U_q(G). In this talk we will explain a (conjectural) extension of this equivalence, where on the Kac-Moody side, instead of G(O)-integrability we impose Iwahori integrability. We will see that on the quantum group side we will have to consider a hybrid between Lusztig's and De Concini-Kac quantum groups.

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School of Science


harmonjo, geo_rep_sem


Department of Mathematics
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