Convex elements and Steinberg's cross-sections
Representation Theory
2024-10-25 v1 Algebraic Geometry
Group Theory
Abstract
In this paper, we study convex elements in a (twisted) Weyl group introduced by Ivanov and the first named author. We show that each conjugacy class of the twisted Weyl group contains a convex element, and moreover, the Steinberg cross-sections exist for all convex elements. This result strictly enlarges the cases of Steinberg cross-sections from a new perspective, and will play an essential role in the study of higher Deligne-Lusztig representations.
Cite
@article{arxiv.2410.18865,
title = {Convex elements and Steinberg's cross-sections},
author = {Sian Nie and Panjun Tan and Qingchao Yu},
journal= {arXiv preprint arXiv:2410.18865},
year = {2024}
}
Comments
11 pages