Fusion Rings of Loop Group Representations

TL;DR

This paper calculates the fusion rings associated with positive energy representations of loop groups for simple, simply connected Lie groups, providing insights into their algebraic structure.

Contribution

It introduces explicit computations of fusion rings for loop group representations of certain Lie groups, advancing understanding in representation theory.

Findings

Explicit fusion ring structures computed

Enhanced understanding of loop group representations

Foundational results for future research

Abstract

We compute the fusion rings of positive energy representations of the loop groups of the simple, simply connected Lie groups.