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

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• 作者：Pramod N. Achar (1)
  Simon Riche (2) (3)
  
  1. Department of Mathematics ; Louisiana State University ; Baton Rouge ; LA ; 70803 ; USA
  2. Clermont Universit茅 ; Universit茅 Blaise Pascal Laboratoire de Math茅matiques ; BP 10448 ; F-63000 ; Clermont-Ferrand ; France
  3. CNRS ; UMR 6620 ; Laboratoire de Math茅matiques ; F-63177 ; Aubi猫re ; France
  
• 刊名：Israel Journal of Mathematics
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：205
• 期：1
• 页码：247-315
• 全文大小：612 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511

文摘

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 \(G({\Bbb C}\left[\kern-0.15em\left[ x \right]\kern-0.15em\right])\) -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.