Algebraic Geometry Seminar: Rationally smooth Schubert varieties and B-modules

Kostant's remarkable formula (which I will recall) generalizes to smooth Schubert varieties in the flag variety G/B of an algebraic group G. On the other hand, Sara Billey noticed that rationally smooth Schubert varieties in G/B give an analogous formula, though it often doesn't agree with the remarkable formula in the singular case. This motivates the question of which rationally smooth Schubert varieties are smooth. I will show that there is a neat answer hinted at in the title.