Grassmann Duality for D-modules

We generalize the main results on projective duality to the case of the correspondence between "dual" Grassmann manifolds G and G*. The new aspect is that the "incidence variety" S subset of G x G* is no longer smooth, a fact which requires the tools of the theory of b-functions. In particular, we obtain an equivalence between the categories of sheaves on G and G*, as well as between those of D-modules; then, quantizing this equivalence, we explicitly calculate the transform of a D-module associated to a holomorphic line bundle.