Irreducible characters of large degree of Sylow p-subgroups of classical groups

Abstract

If G is a Sylow p-subgroup of a classical group defined over a finite field of characteristic p > 2 and G is the associated Lie algebra, we show that the irreducible characters of G with sufficiently large degree p f can be parameterized by the orbits of G on the dual space of G of size p 2 f . We use this correspondence to count the number of irreducible characters of G of maximum degree.