# Divided differences in equivariant K-theory

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stiénon.

**Speaker:** Reyer Sjamaar, Cornell University

**Abstract:** Let X be a topological space and G a compact connected Lie group
acting on X. Atiyah proved that the G-equivariant K-group of X is a
direct summand of the T-equivariant K-group of X, where T is a maximal
torus of G. We show that this direct summand is equal to the subgroup
of K_T^*(X) annihilated by an ideal generated by divided difference
operators. Thus a T-equivariant K-class is G-equivariant if and only
if it is annihilated by certain divided difference operators. If X
consists of a single point, this assertion amounts to the Weyl
character formula. These results generalize when we replace T by a
closed connected subgroup H containing T, provided that we twist
K-theory by a suitable class.
This is joint work with Megumi Harada and Gregory D. Landweber.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/22/2009

**Time:** 2:30pm - 3:30pm