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

In this work we develop 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).