A Combinatorial Approach to Root Multiplicities of a Special Type Rank 3 Kac-Moody Algebras

2021/02/20 by Bowen Chen, Chen, Bowen, Hanyi Luo +3
Mathematics · #17B22 #17B67 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2102.10367

openalex publication_date 2021/02/20 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

Abstract

In this paper, we calculate the dimension of root spaces \mathfrakg_λ of a special type rank 3 Kac-Moody algebras \mathfrakg. We first introduce a special type of elements in \mathfrakg, which we call elements in standard form. Then, we prove that any root space is spanned by these elements. By calculating the number of linearly independent elements in standard form, we obtain a formula for the dimension of root spaces \mathfrakg_λ, which depends on the root λ.

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