Let $G$ be a semi-simple algebraic group over $\mathbb{C}$ with Borel subgroup $B$ and consider the flag variety $G/B$. If $G\_0 \subset G$ is some real form, then $G\_0$ acts on $G/B$ and decomposes the space into a disjoint union of orbits. In the case of $SL\_2$ one gets 2 open orbits while in $SL\_3$ my calculations seem to show a single open orbit. Can one characterize the number of open orbits in general? For what groups is this number larger than 1?



Real orbits of Complex Flag Varieties
[Aomoto (1966)](http://www.ams.org/mathscinet-getitem?mr=191994) gives a formula for the number of open orbits (page 15, between (46) and (47)), and specializes it to various special cases (just search the paper for "open"). 


