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Mathematische Annalen

, Volume 337, Issue 1, pp 197–232 | Cite as

Cartan decomposition of the moment map

  • Peter Heinzner
  • Gerald W. Schwarz
Article

Abstract

We investigate a class of actions of real Lie groups on complex spaces. Using moment map techniques we establish the existence of a quotient and a version of Luna’s slice theorem as well as a version of the Hilbert–Mumford criterion. A global slice theorem is proved for proper actions. We give new proofs of results of Mostow on decompositions of groups and homogeneous spaces.

Mathematics Subject Classification (2000)

32M05 57S20 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr Universität BochumBochumGermany
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA

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