DIVIDED DIFFERENCES AND THE WEYL CHARACTER FORMULA IN EQUIVARIANT K-THEORY

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 certain divided difference operators. If X consists of a single point, this assertion amounts to the Weyl character formula. We also give sufficient conditions on X for K-G*(X) to be isomorphic to the subgroup of Weyl invariants of K-T*(X).