Wienhard: Hermitian symmetric spaces and Kähler rigidity. Transform. Groups

Abstract. We characterize irreducible Hermitian symmetric spaces which are not of tube type both in terms of the topology of the space of triples of pairwise transverse points in the Shilov boundary, and of two invariants which we introduce, the Hermitian triple product and its complexication. We apply these results and the techniques introduced in [6] to characterize conjugacy classes of Zariski dense representations of a locally compact group into the connected component G of the isometry group of an irreducible Her-mitian symmetric space which is not of tube type, in terms of the pullback of the bounded Kahler class via the representation. We conclude also that if the second bounded cohomology of a nitely generated group is nite dimen-sional, then there are only nitely many conjugacy classes of representation