On Root Multiplicities of Some Hyperbolic Kac-Moody Algebras

TL;DR

This paper computes root multiplicities at level three for certain hyperbolic Kac-Moody algebras using coset construction, providing insights into their structure.

Contribution

It introduces a method to calculate specific root multiplicities for hyperbolic Kac-Moody algebras, advancing understanding of their algebraic properties.

Findings

Root multiplicities at level three computed for selected hyperbolic Kac-Moody algebras

Application of coset construction to hyperbolic Kac-Moody algebras

Enhanced understanding of algebraic structure at higher levels

Abstract

Using the coset construction, we compute the root multiplicities at level three for some hyperbolic Kac-Moody algebras including the basic hyperbolic extension of $A_1^{(1)}$ and $E_{10}$.