SMS scnews item created by Anne Thomas at Fri 2 Sep 2011 1206
Type: Seminar
Distribution: World
Expiry: 9 Sep 2011
Calendar1: 9 Sep 2011 1205-1255
CalLoc1: Carslaw 175
Auth: athomas(.pmstaff;2039.2002)@p615.pc.maths.usyd.edu.au

# 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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