Endoscopy for Hecke categories, character sheaves and representations
Abstract
For a split reductive group over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding endoscopic group with trivial monodromy. We also extend this equivalence to all blocks. We give two applications. One is a relationship between character sheaves on with a fixed semisimple parameter and unipotent character sheaves on the endoscopic group , after passing to asymptotic versions. The other is a similar relationship between representations of with a fixed semisimple parameter and unipotent representations of .
Cite
@article{arxiv.1904.01176,
title = {Endoscopy for Hecke categories, character sheaves and representations},
author = {George Lusztig and Zhiwei Yun},
journal= {arXiv preprint arXiv:1904.01176},
year = {2021}
}
Comments
This is a revised version of the paper with the same title published in Forum Math. Pi 8 (2020), e12. An error on a 3-cocycle is corrected and main statements are simplified. A Corrigendum follows the main article. 57 pages