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.