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# Mathematical Research Letters

## Volume 17 (2010)

### Number 3

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

Pages: 507 – 527

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n3.a10

#### Authors

#### 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 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 $K_T^*(X)$.