so let's consider the coadjoint partial flag variety of so(n) and try to see whether we understand the alleged natural contact distribution on it.

so the coadjoint partial flag variety here is the space of rank 2 partial isometries e->f where e,f are euclidean spaces of dimensions m,m+1 respectively if n=2m+1, and of m,m respectively if n=2m, i think.

i'm not seeing it yet...