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| HAL: hal-00700454, version 1 |
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| Geometric Satake, Springer correspondence, and small representations II |
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| Pramod N. Achar 1Anthony Henderson 2 |
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| (2012-05-23) |
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| For a split reductive group scheme $G$ over a commutative ring $k$ with Weyl group $W$, there is an important functor $Rep(G,k) \to Rep(W,k)$ 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 to $G$. 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. |
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| 1: | Department of Mathematics [Baton Rouge] (LSU Mathematics) |
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Louisiana State University |
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| 2: | School of Mathematics and statistics [Sydney] |
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The University of Sydney |
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| 3: | Laboratoire de Mathématiques |
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CNRS : UMR6620 – Université Blaise Pascal - Clermont-Ferrand II |
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| Subject | : | Mathematics/Representation Theory |
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| groupes algébriques réductifs – groupe de Weyl – équivalence de Satake – correspondance de Springer – représentations petites |
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| Attached file list to this document: | |||||
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| hal-00700454, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00700454 | |
| oai:hal.archives-ouvertes.fr:hal-00700454 | |
| From: Simon Riche | |
| Submitted on: Wednesday, 23 May 2012 10:26:50 | |
| Updated on: Wednesday, 23 May 2012 11:29:04 | |
