A remark on the orbit structure of the complexification of a semisimple symmetric space (Q417652)

The author considers the action of a real semisimple group \(G\) on the complexification \(G_{\mathbb{C}}/H_{\mathbb{C}}\) of a semisimple symmetric space \(G/H\). The author gives an explicit construction of ``Cartan subsets'' in the sense of \textit{T. Matsuki} [J. Algebra 197, No.1, 49--91 (1997; Zbl 0887.22009)], which gives ``in principle'' the possibility to parametrize explicitly the \(G\)-orbits of \(G_{\mathbb{C}}/H_{\mathbb{C}}\). The results are stated in terms of Lie algebras, Cartan subspaces and root systems.