Geometric Satake, Springer correspondence and small representations

作者：Achar Pramod N^*; Henderson Anthony

来源：Selecta Mathematica, New Series, 2013, 19(4): 949-986.

DOI：10.1007/s00029-013-0125-7

• Affine Grassmannian
• Nilpotent orbits
• Springer correspondence

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

• 出版日期2013-11