Algebra Seminar: Henderson -- The affine Grassmannian and the nilpotent cone

There will be an Algebra Seminar by Anthony Henderson on Friday 9 September.  

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Speaker: Anthony Henderson (University of Sydney) 

Date: Friday 9 September 

Time: 12.05-12.55pm 

Venue: Carslaw 175 

Title: 

The affine Grassmannian and the nilpotent cone 

Abstract: 

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).  

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