Geometric K-homology and the Freed-Hopkins-Teleman theorem

Abstract: We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group $G$ to the Verlinde ring. Our map is described at the level of D-cycles' for the geometric twisted K-homology of $G$, and is inverse to the Freed-Hopkins-Teleman isomorphism. As an application, we show that two possible definitions of thequantization' of a Hamiltonian loop group space are compatible with each other.