lie_algebras

Computing weight (q)-multiplicities for the representations of the simple Lie algebras. The multiplicity of a weight (mu ) in an irreducible representation of a simple Lie algebra (mathfrak {g}) with highest weight (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 (q)-analog of Kostant’s weight multiplicity and present a SageMath program to compute (q)-multiplicities for the simple Lie algebras.