EVENT DETAILS AND ABSTRACT

Title: Drinfeld-Gaitsgory functor and contragradient duality for (g,K)-modules
Speaker: Alexander Yom Din
Speaker Info: Caltech
Brief Description:
Special Note:
Abstract:

Drinfeld suggested the definition of a certain endo-functor, called the pseudo-identity functor (or the Drinfeld-Gaitsgory functor), on the category of D-modules on an algebraic stack. We extend this definition to an arbitrary DG category, and show that if certain finiteness conditions are satisfied, this functor is the inverse of the Serre functor. We show that the pseudo-identity functor for $(\mathfrak{g},K)$-modules is isomorphic to the composition of cohomological and contragredient dualities, which is parallel to an analogous assertion for p-adic groups.

In this talk I will try to discuss some of these results and around them. This is joint work with Dennis Gaitsgory.