Matsuki's double coset decomposition via gradient maps

Christian Miebach (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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.

Domaines: Théorie des représentations [math.RT]

Christian Miebach. Matsuki's double coset decomposition via gradient maps. Journal of Lie Theory, 2008, 18 (3), pp.555-580. ⟨hal-03600204⟩