Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone
The authors describe the derived category (and a mixed version) of sheaves on the affine Grassmannian of a complex reductive group \(\check{G}\), constructible with respect to the stratification by \(\check{G}(\mathbbx)\)-orbits, in terms of coherent sheaves on the nilpotent cone of the Langlands dual reductive group \(G\). In the mixed case, they show that restriction to the nilpotent cone of a Levi subgroup corresponds to hyperbolic localization on affine Grassmannians.
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