Matsuki's double coset decomposition via gradient maps

Details Matsuki's double coset decomposition via gradient maps Matsuki's double coset decomposition via gradient maps

2007-12-20

arxiv.org/abs/0712.3384v2

Journal of Lie Theory 18 (2008), No. 3, 555--580

Mathematics

Representation Theory

19 pages

Scientific paper

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.

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