Endoscopy for metaplectic affine Hecke categories

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Yau Wing Li (University of Melbourne)

Time：

Fri., 10:30-11:30 am, Dec. 26, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

Endoscopy for metaplectic affine Hecke categories

Abstract:

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. Applications include endoscopic equivalences, the metaplectic derived Satake, and confirming a series conjectured by Gaitsgory in quantum geometric Langlands.