MIT Lie Groups Seminar

Wednesday, February 08, 2023 at 4:00pm to 6:00pm

Building 2, 2-142
182 MEMORIAL DR, Cambridge, MA 02139

Speaker:  Kari Vilonen (University of Melbourne)

Title:  Character sheaves for graded Lie algebras and invariant systems. 

Abstract:  A variant of the nearby cycle construction, due initially to Grinberg, is the main geometric ingredient in our construction of character sheaves for graded Lie algebras. In this talk I will explain this construction and how it allows us to associate character sheaves to representations of Hecke algebras at roots of unity. In particular, I will explain how the Hecke relations arise from appropriate b-functions associated to sections of certain D-modules. The b-functions that arise in our applications can be deduced from previous results of Fumihiro Saito on prehomogenous vector spaces. I will also explain the relationship to invariant systems of differential equations. This is joint work with Ting Xue and Misha Grinberg. 


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