Computing weight q-multiplicities for the representations of the\n simple Lie algebras

2017/10/05 by Pamela E. Harris, Harris, Pamela E., Erik Insko +3
Mathematics · #17-08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1710.02183

openalex publication_date 2017/10/05 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

The multiplicity of a weight \μ in an irreducible representation of a\nsimple Lie algebra mathfrakg with highest weight \λ can be computed\nvia the use of Kostant's weight multiplicity formula. This formula is an\nalternating sum over the Weyl group and involves the computation of a partition\nfunction. In this paper we consider a q-analog of Kostant's weight\nmultiplicity and present a SageMath program to compute q-multiplicities for\nthe simple Lie algebras.\n

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