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

Details Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone

2011-02-14

arxiv.org/abs/1102.2821v1

Mathematics

Representation Theory

62 pages

Scientific paper

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 G(C[[x]])-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 its Langlands dual reductive group. We also show, in the mixed case, that restriction to the nilpotent cone of a Levi subgroup corresponds to hyperbolic localization on affine Grassmannians.

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