Geodesic
Properties of maximums of the multiplicity function
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 1, pp. 99-108
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We redefine the multiplicity function $M(\nu,p)$ for the tensor power $(L^{\omega})^{\otimes p}$ decomposition as a smooth function on the weight space $P_{\mathfrak{g}}$ of a Lie algebra $\mathfrak{g}$ and study the behavior of its maximums. As a result, the submodule with the maximum multiplicity can be easily found for any fixed power $p$.
Keywords: Lie algebra, representation theory, tensor power, integrable model. 
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V. D. Lyakhovsky. Properties of maximums of the multiplicity function. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 1, pp. 99-108. http://geodesic.mathdoc.fr/item/TMF_2013_174_1_a6/

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