Equivalence of Hecke Categories with Deeper Level Structures

Geometry, Symmetry and Physics
Event time: 
Monday, November 13, 2023 - 4:30pm
KT 217
Jianqiao Xia
Speaker affiliation: 
Event description: 

Abstract: Inspired 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.