Geometric Satake, Springer correspondence and small representations

• Pramod N. Achar ^[1] ; Anthony Henderson ^[2]
  1. [1] Louisiana State University

     Louisiana State University

     Estados Unidos

     
  2. [2] University of Sydney

     University of Sydney

     Australia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 19, Nº. 4, 2013, págs. 949-986
• Idioma: inglés
• DOI: 10.1007/s00029-013-0125-7
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• Resumen

  • For a simply-connected simple algebraic group GG over CC , we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of GG , generalizing a well-known fact about GLnGLn . 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.