On the computation of character values for finite Chevalley groups of exceptional type

TL;DR

This paper addresses computational challenges in determining character values of finite Chevalley groups of exceptional type, resolving some open questions related to cuspidal unipotent character sheaves using Lusztig's theory.

Contribution

It provides new computational methods and resolves open questions about roots of unity for cuspidal unipotent character sheaves in exceptional groups.

Findings

Resolved open questions about roots of unity in character sheaves

Enhanced understanding of character values for exceptional Chevalley groups

Applied Lusztig's theory to computational problems in group characters

Abstract

We discuss various computational issues around the problem of determining the character values of finite Chevalley groups, in the framework provided by Lusztig's theory of character sheaves. Some of the remaining open questions (concerning certain roots of unity) for the cuspidal unipotent character sheaves of groups of exceptional type are resolved.