Pham Huu Tiep

University of Florida
 
Title: Globally Irreducible Representations of $SL_{3}(q)$ and $SU_{3}(q)$

Abstract:
  {The notion of globally 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
$PSL_{3}(q)$ and $PSU_{3}(q)$. The main result is that these 
representations are essentially those discovered by Gross.}

The paper has appeared in Israel J. Math. 109 (1999), 225 - 251.