Lie group weight multiplicities from conformal field theory

TL;DR

This paper links Lie group weight multiplicities to conformal field theory modular matrices, revealing symmetries that can determine all multiplicities for certain groups, thus providing a novel algebraic approach.

Contribution

It introduces a method to compute Lie group weight multiplicities using conformal field theory modular matrices, uncovering new symmetry relations that can fully determine multiplicities.

Findings

Modular matrices encode Lie group weight multiplicities.

Symmetries of modular matrices lead to new relations among multiplicities.

For some Lie groups, these relations determine all multiplicities.

Abstract

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.