# A first guide to the character theory of finite groups of Lie type

## TL;DR

This survey introduces Lusztig's work on the character theory of finite groups of Lie type, focusing on parametrization of irreducible characters and results independent of the prime power q.

## Contribution

It provides an accessible overview of Lusztig's character theory, emphasizing parametrization and p,q-independent results, based on lecture series.

## Key findings

- Parametrization of irreducible characters of finite groups of Lie type
- Results valid without restrictions on p or q
- Overview of Lusztig's foundational work

## Abstract

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli (EPFL) in July 2016 and at a summer school in Les Diablerets in August 2015. Our focus here is on questions related to the parametrization of the irreducible characters and on results which hold without any assumption on~$p$ or~$q$.