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

Matsuki's Double Coset Decomposition via Gradient Maps

Christian Miebach
Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, 44780 Bochum, Germany

Let G be a real-reductive Lie group and let G1 and G2 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 G1 \ G / G2 by Cartan subsets. We also describe the elements sitting in non-closed double cosets.

Keywords: Reductive Lie group, involution, orbit structure, gradient map, slice theorem, symmetric Lie algebra.

MSC: 22E15, 22E46

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