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arXiv · 2410.18865

Convex elements and Steinberg's cross-sections

Sian Nie·Panjun Tan·Qingchao Yu
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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.

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BibTeXRIS

Sian Nie, Panjun Tan, Qingchao Yu. 2024-10-24. Convex elements and Steinberg's cross-sections. https://arxiv.org/abs/2410.18865

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