Geodesic
On the caluculation of weight multiplicity
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 251-254
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For each of the classical series of Lie algebras a recursion (in the rank) relation is given for the Kostant partition function. In addition, explicit expressions are given for the partition function of the algebra $G_2$. 
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V. F. Molchanov. On the caluculation of weight multiplicity. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 2, pp. 251-254. http://geodesic.mathdoc.fr/item/TMF_1971_8_2_a8/

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[2] B. Kostant, Matematika (sb. perevodov), 6:1 (1962), 133 | MR

[3] P. Karte, Matematika (sb. perevodov), 6:5 (1962), 135

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[6] T. S. Santhanam, J. Math. Phys., 10 (1969), 1704 | DOI | MR | Zbl

[7] D. Radhakrishnan, J. Math. Phys., 10 (1969), 2129 | DOI | MR | Zbl