Divided differences and the Weyl character formula in equivariant K-theory

Details Divided differences and the Weyl character formula in equivariant K-theory Divided differences and the Weyl character formula in equivariant K-theory

2009-06-09

arxiv.org/abs/0906.1629v2

Math. Res. Lett. 17 (2010), no. 3, 507-527

Mathematics

K-Theory and Homology

22 pages, minor errors corrected, some examples added

Scientific paper

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 $K_T^*(X)$.

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