University of Sydney Algebra Seminar

Yau Wing Li

Friday 10 October, 12-1pm, in Carslaw 175

Endoscopy for metaplectic affine Hecke categories

The Hecke category is central in representation theory. A natural generalization considers sheaves on the enhanced affine flag variety with fixed monodromy along orbits of a centrally extended torus. In joint work with Gurbir Dhillon, Zhiwei Yun, and Xinwen Zhu, we show that these monodromic affine Hecke categories are equivalent to non-monodromic affine Hecke categories of smaller groups, extending results of Lusztig and Yun for finite Hecke categories. In my earlier talk in May I focused more on combinatorial and algebraic aspects; this time I will put more emphasis on the categorical and geometric perspective, with applications to the metaplectic derived Satake and Gaitsgory’s conjectures in the quantum geometric Langlands program.