JournalslemVol. 55, No. 1/2pp. 33–75

On the quantization of conjugacy classes

  • Eckhard Meinrenken

    University of Toronto, Canada
On the quantization of conjugacy classes cover
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Abstract

Let GG be a compact, simple, simply connected Lie group. A theorem of Freed-Hopkins-Teleman identifies the level k0k\ge 0 fusion ring Rk(G)R_k(G) of GG with the twisted equivariant KK-homology at level k+hvk+h^v, where hvh^v is the dual Coxeter number of GG. In this paper, we will review this result using the language of Dixmier-Douady bundles. We show that the additive generators of the group Rk(G)R_k(G) are obtained as KK-homology push-forwards of the fundamental classes of pre-quantized conjugacy classes in GG.

Cite this article

Eckhard Meinrenken, On the quantization of conjugacy classes. Enseign. Math. 55 (2009), no. 1, pp. 33–75

DOI 10.4171/LEM/55-1-2