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Journal Articles Journal de l'Institut de Mathématiques de Jussieu Year : 2015

Differential operators on G/U and the affine Grassmannian

Abstract

We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions: one in terms of D-modules of the basic affine space, and one in terms of intertwining operators for universal Verma modules. We also construct natural collections of isomorphisms parametrized by the Weyl group in these three contexts, and prove that they are compatible with our isomorphisms. As applications we reprove some results of the first author and of Braverman-Finkelberg.
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Dates and versions

hal-00839864 , version 1 (01-07-2013)
hal-00839864 , version 2 (24-03-2014)

Identifiers

  • HAL Id : hal-00839864 , version 2

Cite

Victor Ginzburg, Simon Riche. Differential operators on G/U and the affine Grassmannian. Journal de l'Institut de Mathématiques de Jussieu, 2015, 14. ⟨hal-00839864v2⟩
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