An algorithm for computing root multiplicities in Kac-Moody algebras

TL;DR

This paper introduces an efficient algorithm based on the Peterson recurrence formula for computing root multiplicities in Kac-Moody algebras, which are important in string theory and modular functions.

Contribution

The paper presents a novel, more efficient algorithm for calculating root multiplicities in Kac-Moody algebras using the Peterson recurrence formula.

Findings

The new algorithm outperforms naive methods in efficiency.

Root multiplicities are crucial for understanding Kac-Moody algebra structures.

Applications extend to string theory and modular functions.

Abstract

Root multiplicities encode information about the structure of Kac-Moody algebras, and appear in applications as far-reaching as string theory and the theory of modular functions. We provide an algorithm based on the Peterson recurrence formula to compute multiplicities, and argue that it is more efficient than the naive algorithm.