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Computing weight $$q$$-multiplicities for the representations of the simple Lie algebras. (English) Zbl 1436.17011
Summary: 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.

##### MSC:
 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B20 Simple, semisimple, reductive (super)algebras 17-08 Computational methods for problems pertaining to nonassociative rings and algebras
##### Software:
SageMath; lie_algebras; GitHub
Full Text:
##### References:
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