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