so suppose that we have a total flag f1 and a partial flag x1 and another partial flag x2 of the same type "constructed from f1 and x1". then x2 belongs to the schubert variety given as the closure of the bruhat class "like x1 to f1", and we can ask what's the zariski tangent space of that schubert variety at x2, and there should be some nice answer visible in the root system...