On the Structure of the Fusion Ideal

Abstract

We prove that there is a finite level-independent bound on the number of relations defining the fusion ring of positive energy representations of the loop group of a simple, simply connected Lie group. As an illustration, we compute the fusion ring of $G_2$ at all levels.

References in corpus (9)

• Twisted K-theory and loop group representations
• Loop groups and twisted K-theory I
• On the Twisted K-Homology of Simple Lie Groups
• Presentations of Wess-Zumino-Witten Fusion Rings
• Thom Prospectra for Loopgroup representations
• Loop Groups and Twisted K-Theory II
• On the quantization of conjugacy classes
• Consistent Orientation of Moduli Spaces
• A conjectural presentation of fusion algebras

Cited by in corpus (7)

• Equivariant K-theory of compact Lie group actions with maximal rank isotropy
• Fusion Rings of Loop Group Representations
• The Real K-Theory of Compact Lie Groups
• Equivariant twisted Real $K$-theory of compact Lie groups
• Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy
• $K$-theory of AF-algebras from braided C*-tensor categories
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders