MAXIMAL REPRESENTATIOxxxxxxxxxxxxxNS OF SURFACE GROUPS IN BOUNDED SYMMETRIC DOMAINS
نویسنده
چکیده
Let r be the fundamental group of a hyperbolic surface of genus g; for I ::; p ::; q, PSU(p, q) is the group of isometries of a certain Hermitian symmetric space Dp , q of rank p. There exists a characteristic number c : Hom(r, PSU(p, q)) --+ lR, which is constant on each connected component and such that Ic(p)1 ::; 4pn(g I) for every representation p. We show that representations with maximal characteristic number (plus some nondegeneracy condition if p > 2 ) leave invariant a totally geodesic subspace of D p , q isometric to D p • p •
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