Abstract: Let G be a semi-simple Lie group and \theta be an automorphism
of G, of finite order k. This gives a graduation g = \oplus_i\in Z/kZ
g_i of the Lie algebra g of G, and in particular a representation g_1 of
the group G_0 fixed by \theta. We observe that in many cases, to a
general element of g_1 can be associated an abelian variety embedded in
some (projectivised) fundamental representation of G_0. For instance,
for the group E_8 and some automorphism \theta of order 3, we get G_0 =
SL_9 and g_1 = wedge^3(C^9); to any general point of g_1 is associated a
(3,3)-polarised abelian surface embedded in P_8.

This is a joint work with S. Sam and J. Weyman.