Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone (Q2339733)

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 \(\check{G}(\mathbb[[x]])\)-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.