Geodesic
Matsuki's Double Coset Decomposition via Gradient Maps
Journal of Lie Theory, Tome 18 (2008) no. 3, pp. 555-580

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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.
Classification : 22E15, 22E46
Mots-clés : Reductive Lie group, involution, orbit structure, gradient map, slice theorem, symmetric Lie algebra 
C. Miebach. Matsuki's Double Coset Decomposition via Gradient Maps. Journal of Lie Theory, Tome 18 (2008) no. 3, pp. 555-580. http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a4/
@article{JOLT_2008_18_3_a4,
     author = {C. Miebach},
     title = {Matsuki's {Double} {Coset} {Decomposition} via {Gradient} {Maps}},
     journal = {Journal of Lie Theory},
     pages = {555--580},
     year = {2008},
     volume = {18},
     number = {3},
     zbl = {1171.22003},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a4/}
}
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