QUANTIZATION OF GRASSMANN DUALITY

Let V be a complex vector space of dimension n, G (resp. G) the Grass mann manifold of p-dimensional (resp. (n-p)-dimensional) subspaces of V, and of Omega the relation of transversality in G x G. We announced in [6] equivalences between derived categories of sheaves and of D-mo dules on G and G defined by the integral transforms associated to Ome ga. We show here that these transforms exchange the D-modules associat ed to the holomorphic lines bundles on G and G. This is equivalent to ''quantizing'' the underlying contact transformation between certain open dense subsets of the contangent bundles. In the case p = 1, we re cover already known results for the projective duality (see [1] and [5 ]).