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Cartan decomposition of the moment map

P. Heinzner·G. W. Schwarz
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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.

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P. Heinzner, G. W. Schwarz. 2005-02-24. Cartan decomposition of the moment map. https://arxiv.org/abs/math/0502515

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