Resumen de Geometric Satake, Springer correspondence and small representations

Pramod N. Achar, Anthony Henderson

• 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.