English

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

Representation Theory 2017-10-09 v1

Abstract

The multiplicity of a weight μ\mu in an irreducible representation of a simple Lie algebra g\mathfrak{g} with highest weight λ\lambda can be computed via the use of Kostant's weight multiplicity formula. This formula is an alternating sum over the Weyl group and involves the computation of a partition function. In this paper we consider a qq-analog of Kostant's weight multiplicity and present a SageMath program to compute qq-multiplicities for the simple Lie algebras.

Keywords

Cite

@article{arxiv.1710.02183,
  title  = {Computing weight $q$-multiplicities for the representations of the simple Lie algebras},
  author = {Pamela E. Harris and Erik Insko and Anthony Simpson},
  journal= {arXiv preprint arXiv:1710.02183},
  year   = {2017}
}

Comments

9 pages, code for program, and 5 tables for computation using exceptional Lie algebras