Type: Seminar

Distribution: World

Expiry: 9 Sep 2011

Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

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