Parabolic conjugacy class in finite reductive groups and its additive analogue

TL;DR

This paper explores properties of parabolic conjugacy classes in finite reductive groups and their additive analogues, revealing parallels with Deligne-Lusztig characters and Harish-Chandra induction.

Contribution

It provides new insights into the additive analogue of conjugacy classes, linking finite reductive groups with finite Lie algebra representations.

Findings

Identifies properties of additive analogues of parabolic conjugacy classes

Establishes similarities between Deligne-Lusztig characters and Harish-Chandra induction

Answers a question posed by Goodwin and R"ohrle regarding reductive groups

Abstract

In this paper, we answer the question posed by Goodwin and R\"ohrle for reductive groups and their parabolic subgroups. In addition, we consider an additive analogue of this problem. By studying this additive analogue, we identify similar properties between the Deligne-Lusztig character of a finite reductive group and the Harish-Chandra induction over the corresponding finite Lie algebra.