Globally irreducible representations of SL3(q) and SU3(q)

The notion of globally irreducible representations of finite groups was int roduced by B. H. Gross, in order to explain new series of Euclidean lattice s discovered by N. Elkies and T. Shioda using Mordell-Well lattices of elli ptic curves. In this paper we classify all globally irreducible representat ions coming from projective complex representations of the finite simple gr oups PSL3(q) and PSU3(q). The main result is that these representations are essentially those discovered by Gross.