Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Special Issue: In Memory of Prof. Bertram Kostant
Guest Editors: Shrawan Kumar, Lizhen Ji, and Kefeng Liu
From conjugacy classes in the Weyl group to semisimple conjugacy classes
Pages: 1159 – 1189
Suppose $G$ is a connected complex semisimple group and $W$ is its Weyl group. The lifting of an element of $W$ to $G$ is semisimple. This induces a well-defined map from the set of elliptic conjugacy classes of $W$ to the set of semisimple conjugacy classes of $G$. In this paper, we give a uniform algorithm to compute this map. We also consider the twisted case.
algebraic groups, Weyl groups, elliptic conjugacy classes, semisimple conjugacy classes
2010 Mathematics Subject Classification
Primary 20G07. Secondary 20E45, 20F55.
To Bert Kostant with admiration.
X. H. was partially supported by NSF DMS-1801352.
S. N. is supported in part by QYZDB-SSW-SYS007 and NSFC grant (Nos. 11501547, 11621061 and 11688101).
Received 11 March 2019
Accepted 26 March 2020
Published 22 December 2021