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

The notion ofglobally irreducible representations of finite groups was introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered by N. Elkies and T. Shioda using Mordell-Weil lattices of elliptic curves. In this paper we classify all globally irreducible representations coming from projective complex representations of the finite simple groups PSL₃(q) and PSU₃(q). The main result is that these representations are essentially those discovered by Gross.