Twisted K-theory and loop group representations

Abstract

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations of the loop groups. Here, we treat arbitrary compact Lie groups. In addition, we discuss the relation to semi-infinite cohomology, the fusion product of Conformal Field theory, the rôle of energy and the topological Peter-Weyl theorem.

The final SELF-CONTAINED version is v.2. The current version had some material removed to the prequels [FHT1,2]. Minor notational changes