Geodesic
Weight $q$-multiplicities for representations of $\mathfrak{sp}_4(\mathbb{C})$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 494-502

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In this paper we present a closed formula for the values of the $q$-analog of Kostant's partition function for the Lie algebra $\mathfrak{sp}_4(\mathbb{C})$ and use this result to give a simple formula for the $q$-multiplicity of a weight in the representations of the Lie algebra $\mathfrak{sp}_4(\mathbb{C})$. This generalizes the 2012 work of Refaghat and Shahryari that presented a closed formula for weight multiplicities in representations of the Lie algebra $\mathfrak{sp}_4(\mathbb{C})$.
Keywords: Sympletic Lie algebra, $q$-analog of Kostant partition function, weight multiplicity, weight $q$-multiplicity.
Mots-clés : Kostant partition functions 
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     title = {Weight $q$-multiplicities for representations of $\mathfrak{sp}_4(\mathbb{C})$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Pamela E. Harris; Edward L. Lauber. Weight $q$-multiplicities for representations of $\mathfrak{sp}_4(\mathbb{C})$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 494-502. http://geodesic.mathdoc.fr/item/JSFU_2017_10_4_a9/