Let be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level fusion ring of with the twisted equivariant -homology at level , where is the dual Coxeter number of . In this paper, we will review this result using the language of Dixmier-Douady bundles. We show that the additive generators of the group are obtained as -homology push-forwards of the fundamental classes of pre-quantized conjugacy classes in .
Cite this article
Eckhard Meinrenken, On the quantization of conjugacy classes. Enseign. Math. 55 (2009), no. 1/2, pp. 33–75DOI 10.4171/LEM/55-1-2