Finding Characters Satisfying a Maximal Condition for Their Unipotent Support

TL;DR

This paper extends previous results on the existence of irreducible characters in finite reductive groups, focusing on their unipotent support and related semisimple elements, providing new insights into their numerical relationships.

Contribution

It introduces new findings on characters satisfying maximal conditions related to unipotent support and explores properties of quasi-isolated semisimple elements.

Findings

Existence of irreducible characters with specific unipotent support properties

Results on quasi-isolated semisimple elements

Extension of Lusztig and Hézard's prior results

Abstract

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a strong numerical relationship with their unipotent support. Along the way we obtain some results concerning quasi-isolated semisimple elements.