Properties of maximums of the multiplicity function

V. D. Lyakhovsky

St. Petersburg State University, St. Petersburg, Russia

Abstract: 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.

DOI: 10.4213/tmf8354

 English version: Theoretical and Mathematical Physics, 2013, 174:1, 86–94

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