## Grassmann duality for $${\mathcal D}$$-modules. (La dualité de Grassmann pour les $${\mathcal D}$$-modules.)(French. Abridged English version)Zbl 0860.32005

Author’s summary: “Let $$\mathbb{G}$$ and $$\mathbb{G}^*$$ be two Grassmann manifolds of subspaces of complementary dimensions in a complex vector space, and let $$\Omega$$ be the open subset of transversal pairs in $$\mathbb{G} \times \mathbb{G}^*$$. Generalizing results of J.-L. Brylinski [Astérisque 140-141, 3-134 (1986; Zbl 0624.32009)], A. D’Agnolo and P. Schapira [C. R. Acad. Sci., Paris, Sér. I 319, No. 6, 595-598 (1994; Zbl 0832.32013)] and M. Kashiwara and T. Tanisaki [Duke Math. J. 77, No. 1, 21-62 (1995; Zbl 0829.17020)] for projective duality, we show that the integral transform defined by the constant sheaf on $$\Omega$$ is an equivalence between the bounded derived categories of sheaves on $$\mathbb{G}$$ and $$\mathbb{G}^*$$ with $$\mathbb{R}$$- or $$\mathbb{C}$$-constructible cohomology. Moreover the integral transform given by the associated regular holonomic kernel is an equivalence between bounded derived categories of $$\mathcal D$$-modules on $$\mathbb{G}$$ and $$\mathbb{G}$$ with coherent or regular holonomic cohomology”.

### MSC:

 32C38 Sheaves of differential operators and their modules, $$D$$-modules 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials

### Citations:

Zbl 0624.32009; Zbl 0832.32013; Zbl 0829.17020