Transformation Groups

, Volume 12, Issue 1, pp 5–32

Hermitian symmetric spaces and Kahler rigidity

Article

DOI: 10.1007/s00031-005-1135-0

Cite this article as:
Burger, M., Iozzi, A. & Wienhard, A. Transformation Groups (2007) 12: 5. doi:10.1007/s00031-005-1135-0
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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].

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