If $G$ is a complex semisimple Lie group,and $B$ is a Borel group, we can form the flag variety $G/B$. If $G\_R$ is a real form of $G$, we can then let $G\_R$ act of $G/B$ on the left and consider the orbit space $G\_R\setminus G/B$. I have seen discussions of the open orbits, but is there a reference that classifies all the orbits? In particular I am interested in the case $SL\_n(H)\setminus SL\_{2n}(C)/B$



real orbits on flag varieties
Classic paper: Joseph A. Wolf (1969), [*The action of a real semisimple group on a complex flag manifold. I. Orbit structure and holomorphic arc components.*](http://www.ams.org/mathscinet-getitem?mr=251246)


Recent survey: Dmitri Akhiezer (2013), [*Real group orbits on flag manifolds.*](http://www.ams.org/mathscinet-getitem?mr=3186684)


