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

E. Vasserot
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Abstract

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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E. Vasserot. 2000-05-02. On the action of the dual group on the cohomology of perverse sheaves on the affine grassmannian. https://arxiv.org/abs/math/0005020

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