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Transformation Groups

, Volume 12, Issue 1, pp 5–32 | Cite as

Hermitian symmetric spaces and Kahler rigidity

  • Marc Burger
  • Alessandra Iozzi
  • Anna Wienhard
Article

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].

Keywords

Symmetric Space Parabolic Subgroup Tube Type Hermitian Symmetric Space Geodesic Triangle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

  1. 1.FIM, ETH Zentrum, Ramistrasse 101, CH-8092ZurichSwitzerland
  2. 2.Institut fur Mathematik, Universitat Basel, Rheinsprung 21, CH-4051BaselSwitzerland
  3. 3.Department de Mathematiques, Universite de Strasbourg, 7 rue Rene Descartes, F-67084Strasbourg CedexFrance
  4. 4.School of Mathematics, Institute for Advanced Study, 1 Einstein DrivePrinceton, NJ 08540USA
  5. 5.Department of Mathematics, University of Chicago, 5734 S. University Ave.Chicago, IL 60637USA

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