Constructing characters of Sylow p-subgroups of finite Chevalley groups

Abstract

Let q be a power of a prime p, let Gbe a finite Chevalley group over Fqand let Ube a Sylow p-subgroup ofG; we assume that pis not a very bad prime forG. We explain a procedure of reduction of irreducible complex characters ofU, which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters ofUalong with a means to construct these characters as induced characters. Afocus in this paper is determining the parametrization when Gis of type F4, where we observe that the parametrization is "uniform"? over good primes p >3, but differs for the bad prime p =3. We also explain how it has been applied for all groups of rank 4or less.