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 crosssections 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.

Publication:

Advances in Mathematics Volume 475, July 2025, 110346 http://dx.doi.org/10.1016/j.aim.2025.110346

Author:

Sian Nie

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

School of Mathematical Sciences, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing 100049, China

Corresponding author

niesian@amss.ac.cn

Panjun Tan

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

tanpanjun@amss.ac.cn

Qingchao Yu

Institute for Advanced Study, Shenzhen University, Shenzhen 518060, Guangdong, China

qingchao_yu@outlook.com