ENDOSCOPY FOR HECKE CATEGORIES, CHARACTER SHEAVES AND REPRESENTATIONS
Name
endoscopy-for-hecke-categories-character-sheaves-and-representations.pdf
Description
Published version
Size
1023.78 KB
Format
Adobe PDF
Checksum (MD5)
69791b0886c95d5ad0d515392bb87548
Author(s)
LUSZTIG, GEORGE
YUN, ZHIWEI
Date Issued
2020
Journal
Forum of Mathematics, Pi
Publisher
Cambridge University Press (CUP)
Version
Final published version
Abstract
© 2020 Journal of Materials Research. All rights reserved. For a 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1017/FMP.2020.9
