Hermitian symmetric spaces and Kahler rigidity |
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Authors: | Marc Burger Alessandra Iozzi Anna Wienhard |
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Institution: | (1) FIM, ETH Zentrum, Ramistrasse 101, CH-8092, Zurich, Switzerland;(2) Institut fur Mathematik, Universitat Basel, Rheinsprung 21, CH-4051, Basel, Switzerland;(3) Department de Mathematiques, Universite de Strasbourg, 7 rue Rene Descartes, F-67084, Strasbourg Cedex, France;(4) School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA;(5) Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637, USA |
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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 complexification. 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 Hermitian 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 finitely generated
group Γ is finite dimensional, then there are only finitely many conjugacy classes of representations of Γ into G with Zariski
dense image. This generalizes results of 6]. |
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