Twisted K-Theory of Lie Groups

TL;DR

This paper computes the twisted K-theory of all compact simply connected simple Lie groups, linking it to conformal field theory via the Freed-Hopkins-Teleman theorem, and discusses exceptions noted in prior work.

Contribution

It provides a complete computation of twisted K-theory for these Lie groups and clarifies the connection to conformal field theory, including analysis of known exceptions.

Findings

Confirmed the twisted K-theory matches CFT predictions

Identified specific exceptions in the theory

Validated the Freed-Hopkins-Teleman theorem application

Abstract

I determine the twisted K-theory of all compact simply connected simple Lie groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze the exceptions noted by Bouwknegt et al.