Divided differences in equivariant K-theory
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
Time: 2:30pm - 3:30pm