i think that i understand a bit better now the relationship between "tangent spaces of schubert varieties" and "invariant distributions on flag varieties...

one of the examples that had been bugging me for quite a while concerns the b2 grassmanian whose 2d schubert variety has a basepoint singularity. on the one hand, it seemed nearly irresistible to match up the 4 schubert varieties on the grassmanian (0d, 1d, 2d, and 3d) with the 4 submodules (0d "-", 1d "g", 2d "gh", 3d "ghi") of the "ghi" module of the "abcde" borel subalgebra (referring to a primitive picture of the b2 root system as follows:

abc
def
ghi

). but on the other hand, the basepoint singularity of the 2d schubert variety means that its zariski tangent space at the basepoint must be 3d, so the obvious straigthforward "irresistible" match-up can't be quite correct.

i think that i have this more or less straightened out now, though. you can picture the module "ghi" as the tangent space at a point of the projective light cone of pseudo-euclidean (2,3)-space. this projective light cone itself carries a (1,2)-signature conformal structure encoded as a field of light cones on its tangent spaces. so the module "ghi" is a 3d vector space equipped with a light cone, and further equipped with a favorite light ray through the origin, the remnant of a light ray in the projective light cone... the 1d submodule "g" is the favorite light ray, but what had been confusing me was the 2d submodule "gh". now it seems clear that it's "the plane tangent to the light cone and containing the favorite light ray", which is subtly different from but morally close to "the tangent space of the 2d schubert variety at the basepoint". this moral closeness seems like a big hint as to what's realy going on here...

by the way john huerta pointed out that this "plane tangent to the light cone and containing the favorite light ray can also be thought of as the pseudo-euclidean orthogonal "complement" of the favorite light ray. that seems interesting, though i'm not sure what to make of it yet...