Computing weight $q$-multiplicities for the representations of the simple Lie algebras
Representation Theory
2017-10-09 v1
Abstract
The multiplicity of a weight in an irreducible representation of a simple Lie algebra with highest weight 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 -analog of Kostant's weight multiplicity and present a SageMath program to compute -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