A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras

TL;DR

This paper introduces a combinatorial method using Dyck paths to analyze root multiplicities in rank 2 hyperbolic Kac-Moody algebras, providing new insights into their structure.

Contribution

It presents a novel combinatorial approach to compute root multiplicities, advancing understanding of rank 2 hyperbolic Kac-Moody algebra structures.

Findings

Dyck path combinatorics effectively models root multiplicities

New formulas for root multiplicities in rank 2 hyperbolic Kac-Moody algebras

Enhanced understanding of algebraic structure through combinatorial methods

Abstract

In this paper we study root multiplicities of rank 2 hyperbolic Kac-Moody algebras using the combinatorics of Dyck paths.