Irreducible brauer characters of the 3-dimensional special unitary groups in non-defining characteristic∗

Abstract

The purpose of this paper is to study the r-modular Brauer character of the special unitary groups SU(3, q²) for odd primes r not dividing q. It turns out that we encounter unexpected difficulties in the principal r-block in the case r‖q + 1. Some ways are described how to attack this problem, which are at least sufficient to solve the problem for an infinite number of prime powers q.