GRASSMANN DUALITY FOR D-MODULES

We generalize the main results on projective duality (see [2], [4], [1 2]) to the case of the correspondence between ''dual'' Grassmann manif olds G and G. The new aspect is that the ''incidence variety'' S subs et of G x G is no longer smooth, a fact which requires the tools of t he theory of b-functions ([7], [17]). In particular, we obtain an equi valence between the categories of sheaves on G and G, as well as betw een those of D-modules; then, quantizing this equivalence, we explicit ly calculate the transform of a D-module associated to a holomorphic l ine bundle. (C) Elsevier, Paris.