hmm, googling on "tangent space of a schubert variety" doesn't give that many hits but it gives a few suggestive ones (that of course i only glanced at and didn't really read yet because as usual i feel that i need to try to figure things out for myself or i won't understand them, for the most part)... in particular a buzzword "pattern avoidance" showed up... i think that i have a vague memory of hearing of that before (could be misremembering though) in connection with coxeter complexes and so forth (or something...)... in the back of my mind i think that i was even guessing that it might show up here, even though i have almost no idea what it means yet...

on the other hand, it does somewhat sound like too complicated an idea to be showing up in this context... i have the feeling that this tangent space of schubert variety stuff is basically very simple and doesn't particularly need any complicated ideas...