Geometric Satake, Springer Correspondence, and Small Representations Ii
نویسندگان
چکیده
Abstract. For a split reductive group scheme Ǧ over a commutative ring k with Weyl group W , there is an important functor Rep(Ǧ, k) → Rep(W, k) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dual group G. The translation from representation theory to geometry is via the Satake equivalence and the Springer correspondence. This generalizes the result for the k = C case proved by the first two authors, and also provides a better explanation than in that earlier paper, since the current proof is uniform across all types.
منابع مشابه
Geometric Satake, Springer Correspondence, and Small Representations
For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...
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