# real orbits on flag varieties

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 $SL_n(H)\setminus SL_{2n}(C)/B$

• This is good but what I really would like is an exact characterization of the orbits, and if I'm not mistaken these sources only give an upper bound. In particular the first source (page 1131) gives some orbits indexed by $P_{\phi}$ and then says they may not be distinct. Is there some way to tell which of these are equal to each other? – A.D. Sep 8 '16 at 19:30