In this paper we study the derived category of sheaves on the affine Grassmannian of a complex reductive group G, contructible with respect to the stratification by (Formula presented.)-orbits. Following ideas of Ginzburg and Arkhipov-Bezrukavnikov-Ginzburg, we describe this category (and a mixed version) in terms of coherent sheaves on the nilpotent cone of the Langlands dual reductive group G. We also show, in the mixed case, that restriction to the nilpotent cone of a Levi subgroup corresponds to hyperbolic localization on affine Grassmannians.
Publication Source (Journal or Book title)
Israel Journal of Mathematics
Achar, P., & Riche, S. (2015). Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone. Israel Journal of Mathematics, 205 (1), 247-315. https://doi.org/10.1007/s11856-014-1132-x