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

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Abstract

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.

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Correspondence to Pamela E. Harris.

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The first and third author were supported by NSF award DMS-1620202.

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Harris, P.E., Insko, E. & Simpson, A. Computing weight q-multiplicities for the representations of the simple Lie algebras. AAECC 29, 351–362 (2018). https://doi.org/10.1007/s00200-017-0346-7

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  • DOI: https://doi.org/10.1007/s00200-017-0346-7

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