Matsuki's double coset decomposition via gradient maps

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Miebach, Christian
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Let $G$ be a real-reductive Lie group and let $G_1$ and $G_2$ be two subgroups given by involutions. We show how the technique of gradient maps can be used in order to obtain a new proof of Matsuki's parametrization of the closed double cosets $G_1\backslash G/G_2$ by Cartan subsets. We also describe the elements sitting in non-closed double cosets.
Comment: 19 pages
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Mathematics - Representation Theory
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