Geometric Satake, Springer correspondence, and small representations
by Pramod Achar
Abstract: This talk is concerned with a kind of "compatibility" between two deep results in geometric representation theory: the geometric Satake isomorphism and the Springer correspondence. Both of these involve realizing representations (of a reductive group G and its Weyl group W, respectively) in terms of perverse sheaves on some variety (the dual affine Grassmannian Gr and the nilpotent cone N, respectively). I will explain how the geometry of N is related to that of Gr, as well as what this implies on the representation-theoretic side. For the latter, the notion of "small representations," which has been studied by Broer and Reeder, plays a key role. This is joint work with A. Henderson and S. Riche.