Constructing characters of Sylow p-subgroups of finite Chevalley groups.

Let q be a power of a prime p , let G be a finite Chevalley group over F q and let U be a Sylow p -subgroup of G ; we assume that p is not a very bad prime for G . We explain a procedure of reduction of irreducible complex characters of U , which leads to an algorithm whose goal is to obtain a parametrization of the irreducible characters of U along with a means to construct these characters as induced characters. A focus in this paper is determining the parametrization when G is of type F 4 , 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 4 or less. [ABSTRACT FROM AUTHOR]