so it seems like it should be easy to find a partial flag variety with no invariant (under the "whole" group, that is) contact distribution...

so for example, let's consider the projective plane as a partial flag variety of a2...
it seems pretty clear that this has no nontrivial invariant distribution at all...

now is there any projective coadjoint orbit of the split real form (for example...) that's equivalent as a homogeneous space to the projective plane??

??hmmm, perhaps not??

on the other hand, what about the total flag variety of a3? has it got an invariant contact distribution? perhaps there _is_ a coadjoint orbit equivalent to it??

0 0 0
1 0 0
0 1 0

????.....

??so what _are_ the projective coadjoint oribts of a2 like in general??