The present contribution is the written counterpart of a talk given in Yerevan at the SQS’2019 International Workshop “Supersymmetries and Quantum Symmetries” (SQS’2019, 26 August–August 31, 2019). After a short presentation of various pictographs (O-blades, metric honeycombs) that one can use in order to calculate \({\text{SU}}(n)\) multiplicities (Littlewood–Richardson coefficients, Kostka numbers), we briefly discuss the semi-classical limit of these multiplicities in relation with the Horn and Schur volume functions and with the so-called \({{R}_{n}}\)-polynomials that enter the expression of volume functions. For \(n \leqslant 6\) the decomposition of the \({{R}_{n}}\)-polynomials on Lie group characters is already known, the case \(n = 7\) is obtained here.

中文翻译：

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多重性，象形文字和卷

本文稿是在埃里温在SQS'2019国际研讨会“超对称和量子对称”（SQS'2019，2019年8月26日至2019年8月31日）上的演讲的书面对应内容。在简短介绍了各种象形图（O形刀片，公制蜂窝）后，人们可以使用它们来计算\（{\ text {SU}}（n）\）乘数（Littlewood–Richardson系数，Kostka数）讨论与Horn和Schur体积函数以及进入体积函数表达式的所谓\（{{R} _ {n}} \）多项式有关的这些多重性的半经典极限。对于\（n \ leqslant 6 \），已经知道Lie组字符上的\（{{R} _ {n}} \）多项式的分解，在这里获得了\（n = 7 \）。