# Anthony Henderson (University of Sydney)

## Friday 9 September, 12:05-12:55pm, Carslaw 175

### The affine Grassmannian and the nilpotent cone

Let $$G$$ be a simply-connected simple algebraic group over $$\mathbb{C}$$. The geometric Satake correspondence is a category equivalence between representations of the dual group $$G^\vee$$ and $$G(\mathbb{C}[[t]])$$-equivariant perverse sheaves on the affine Grassmannian of $$G$$. The Springer correspondence is an equivalence between representations of the Weyl group $$W$$ and a subcategory of $$G$$-equivariant perverse sheaves on the nilpotent cone of $$G$$. The obvious functor from representations of $$G^\vee$$ to representations of $$W$$, namely taking invariants for the maximal torus, seems difficult to describe in geometric terms. However, I will explain a simple description of the restriction of this functor to the category of "small" representations of $$G^\vee$$, in terms of a new relationship between the "small part" of the affine Grassmannian and the nilpotent cone. This is joint work with Pramod Achar (Louisiana State University).