Twisted K-theory and loop group representations

TL;DR

This paper extends the relationship between equivariant twisted K-theory and loop group representations to all compact Lie groups, exploring connections to semi-infinite cohomology, fusion products, and the topological Peter-Weyl theorem.

Contribution

It generalizes previous results to arbitrary compact Lie groups and discusses their relation to various structures in conformal field theory and topology.

Findings

Established the link between twisted K-theory and loop group representations for all compact Lie groups.

Explored the connections to semi-infinite cohomology and fusion products.

Analyzed the role of energy and the topological Peter-Weyl theorem in this context.

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 r\^ole of energy and the topological Peter-Weyl theorem.