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
christian.miebach@ruhr-uni-bochum.de
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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