On the quantization of conjugacy classes

Abstract

Let G be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k\ge 0 fusion ring R_k(G) of G with the twisted equivariant K -homology at level k+h^v , where h^v is the dual Coxeter number of G . In this paper, we will review this result using the language of Dixmier-Douady bundles. We show that the additive generators of the group R_k(G) are obtained as K -homology push-forwards of the fundamental classes of pre-quantized conjugacy classes in G .