Geodesic
Kostant partition function for $\mathfrak{sp}_4(\mathbb C)$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 18-24.

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In this note, we obtain exact values of the partition function of Kostant for the simple Lie algebra $\mathfrak{sp}_4(\mathbb C)$. Using the values of the partition function, we can find the weight multiplicities of irreducible representations of $\mathfrak{sp}_4(\mathbb C)$ by a simple computation.
Keywords: symplectic Lie algebra, Kostant partition function, Weyl group, weight multiplicity. 
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Hasan Refaghat; Mohammad Shahryari. Kostant partition function for $\mathfrak{sp}_4(\mathbb C)$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 1, pp. 18-24. http://geodesic.mathdoc.fr/item/JSFU_2012_5_1_a1/

[1] R. W. Carter, Lie algebras of finite and affine type, Cambridge University Press, 2005 | MR | Zbl