ok, so after just talking to chris rogers about it a bit, the story of the invariant contact distribution on the "coadjoint partial flag variety" of a simple lie algebra seems to be getting clearer.

when i first started noticing these invariant contact distributions and the heisenberg subalgebras associated with them, before i realized that they were associated with the symplectic structure on coadjoint orbits, i referred to these heisenberg subalgebras as "hidden heisenbergs". only now am i finally realizing just how un-hidden they are; they always lie right at any "corner" of a root system, being the killing-orthogonal complement of the stabilizer of the extremal weight space (thought of as a point of the coadjoint partial flag variety) at the opposite corner. (it looks like you can think of a simple lie algebra as sort of "pasted together" from the heisenberg subalgebras at its corners plus the cartan subalgebra in the middle, but i don't really know what to make of that yet.) the fact that they're so un-hidden suggests of course that they must already be well-known and well-understood, so i'm a bit surprised that i don't think that i've heard about them.

hmm, is a simple lie algebra always generated by the heisenberg algebra associated with a long root and the copy of sl(2) assocated with it, and is there some nice way of presenting the simple lie algebra arising from this?

one question that bugs me a bit at the moment is this: the coadjoint partial flag variety of a simple lie algebra x is a quotient space of a certain coadjoint orbit; what (if any) irrep of x arises from "geometric quantization" of that coadjoint orbit??

also... ??we can interpret this coadjoint orbit as an adjoint orbit (because of the nondegeneracy of the killing form, right?) and then obtain a conjugacy class by exponentiation... hmm, i was going to try to relate this conjugacy class to yet another partial flag variety, but... again i'm being sloppy about different forms of the lie algebra... compact vs complex vs split real.... ??.... it seems pretty clear that this kind of sloppiness is causing confusion with the previous question too...