The Verlinde algebra is twisted equivariant K-theory

TL;DR

This paper explores a new description of the Verlinde algebra using twisted equivariant K-theory, providing insights for compact Lie groups and linking to topological field theory.

Contribution

It introduces a novel perspective on the Verlinde algebra through twisted K-theory and proves the case for SU(2), setting the stage for the general theorem.

Findings

Verlinde algebra can be described via twisted equivariant K-theory

Proof provided for the SU(2) case

Connections to topological field theory are established

Abstract

In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate the general theorem using ideas in topological field theory. The full proof will appear elsewhere.