Speaker:  Tsao Hsien Chen (University of Minnesota)

Title: Mars-Springer slices for loop spaces of symmetric varieties

Abstract: Let X be a symmetric variety.  J. Mars and T. Springer constructed conical transversal slices to the closure of Borel orbits on X and used them to show that the IC-complexes for the orbit closures are  pointwisepure. This is an important geometric ingredient in their work on Hecke algebra representations associated to symmetric varieties providing a more geometric approach to the results of Lusztig-Vogan.

In the talk, I will discuss a generalization of Mars-Springer's construction of transversal slices to the setting of the loop space LX of X where we consider closures of spherical orbits on LX. I will explain applications to relative Langlands duality. If time permits, I will  discuss the case of closures of Iwahori orbits on LX. This is a joint work with Lingfei Yi.