MIT Lie Groups Seminar

Wednesday, February 21, 2024 at 4:00pm to 6:00pm

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

Speaker:  Jianqiao Xia (Harvard University)

Title:  Equivalence of Hecke Categories with Deeper Level Structures

AbstractInspired by the theory of positive depth representations of p-adic reductive groups, we study Hecke categories associated to certain open compact subgroups smaller than the Iwahori subgroup. In this talk, I will prove that in some cases these  Hecke categories are monoidally equivalent to affine Hecke categories of smaller groups, therefore having applications to the local geometric Langlands correspondence. Using sheaf-function correspondence, our categorical equivalence recovers a family of Hecke algebra isomorphisms already proven by Ju-Lee Kim.  

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