2020/08/10 by Krishanu Roy, Roy, Krishanu
Mathematics · #17B10 #17B67 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:17B10 #msc:17B67
paper · pdf · doi:10.48550/arxiv.2008.04173
16 pages
arxiv created 2020/08/10 · openalex publication_date 2020/08/10 · arxiv updated 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dual space of the Cartan subalgebra in a Kac-Moody algebra has a partial ordering defined by the rule that two elements are related if and only if their difference is a non-negative or non-positive integer linear combination of simple roots. In this paper, we study the subposet formed by dominant weights in affine Kac-Moody algebras. We give a more explicit description of the covering relations in this poset. We also study the structure of basic cells in this poset of dominant weights for untwisted affine Kac-Moody algebras of type A.