Character ratios, representation varieties and random generation of finite groups of Lie type

TL;DR

This paper leverages character theory of finite groups of Lie type to derive new insights into their representation varieties and probabilistic generation, advancing understanding of their algebraic and probabilistic properties.

Contribution

It introduces novel results connecting character theory with the structure and generation of finite groups of Lie type.

Findings

New results on representation varieties of Fuchsian groups

Probabilistic generation results for groups of Lie type

Enhanced understanding of algebraic and probabilistic properties

Abstract

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.