Geometric Satake, Springer Correspondence, and Small Representations
نویسنده
چکیده
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 of known facts (mostly due to Broer and Reeder) about small representations of the dual group.
منابع مشابه
Geometric Satake, Springer Correspondence, and Small Representations Ii
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 dua...
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