# On the characters of Sylow $p$-subgroups of finite Chevalley groups $G(p^f)$ for arbitrary primes

## TL;DR

This paper introduces a new method to parametrize irreducible characters of Sylow p-subgroups in finite Chevalley groups for any prime, including very bad primes, and applies it to G=F4(2^f).

## Contribution

It develops a universal parametrization method for irreducible characters of Sylow p-subgroups applicable to all primes, including very bad primes.

## Key findings

- Parametrization method valid for arbitrary primes p.
- Explicit parametrization for G=F4(2^f).
- Enhanced understanding of Sylow p-subgroup characters.

## Abstract

We develop in this work a method to parametrize the set $\mathrm{Irr}(U)$ of irreducible characters of a Sylow $p$-subgroup $U$ of a finite Chevalley group $G(p^f)$ which is valid for arbitrary primes $p$, in particular when $p$ is a very bad prime for $G$. As an application, we parametrize $\mathrm{Irr}(U)$ when $G=\mathrm{F}_4(2^f)$.