On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian

Details On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian

2000-05-02

arxiv.org/abs/math/0005020v1

Mathematics

Algebraic Geometry

AMS-TeX, 9 pages

Scientific paper

It was proved by Ginzburg and Mirkovic-Vilonen that the $G(O)$-equivariant perverse sheaves on the affine grassmannian of a connected reductive group $G$ form a tensor category equivalent to the tensor category of finite dimensional representations of the dual group $G^\vee$. The proof use the Tannakian formalism. The purpose of this paper is to construct explicitely the action of $G^\vee$ on the global cohomology of a perverse sheaf.

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