Journal of Lie Theory

no. 3
Matsuki's Double Coset Decomposition via Gradient Maps
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 555-580
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.
DOI: 10.5802/jolt.511
Classification: 22E15, 22E46
Keywords: Reductive Lie group, involution, orbit structure, gradient map, slice theorem, symmetric Lie algebra 
@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},
     doi = {10.5802/jolt.511},
     zbl = {1171.22003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.511/}
}
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%J Journal of Lie Theory
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C. Miebach. Matsuki's Double Coset Decomposition via Gradient Maps. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 555-580. doi: 10.5802/jolt.511

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