WEIL REPRESENTATIONS AS GLOBALLY IRREDUCIBLE REPRESENTATIONS

The notion of globally irreducible representations of finite groups wa s introduced by B. H. GROSS, in order to explain new series of Euclide an lattices discovered recently by N. ELKIES and T. SHIODA using Morde ll-Weil lattices of elliptic curves. It has been observed by R. Gow an d GROSS that irreducible Well representations of certain finite classi cal groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Well representations of finite classical groups.