Large tensor products and Littlewood-Richardson coefficients
Large tensor products and Littlewood-Richardson coefficients
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大张量积和 Littlewood-Richardson 系数
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
E. Feigin
中科院分区：
文献类型：
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作者：
E. Feigin
Littlewood-Richardson系数描述了简单李代数的不可约表示的张量积分解为不可约表示。假设因子的数量很大，人们可以在权重空间上得到一个度量。许多作者对这一限制措施进行了广泛研究。特别是，Kerov计算了相应的密度在一个特殊情况下，A型和Kuperberg给出了一个公式的一般情况。本文的目的是给出极限测度密度公式的一个简短、完备的纯李理论证明。我们的方法是基于由Littlewood-Richardson系数引起的极限测度和由张量积的重数定义的测度之间的联系。
The Littlewood-Richardson coefficients describe the decomposition of tensor products of irreducible representations of a simple Lie algebra into irreducibles. Assuming the number of factors is large, one gets a measure on the space of weights. This limiting measure was extensively studied by many authors. In particular, Kerov computed the corresponding density in a special case in type A and Kuperberg gave a formula for the general case. The goal of this paper is to give a short, self-contained and pure Lie theoretic proof of the formula for the density of the limiting measure. Our approach is based on the link between the limiting measure induced by the Littlewood-Richardson coefficients and the measure defined by the weight multiplicities of the tensor products.
简单李代数表示的大张量积中不可约重数
影响因子：
1.2
作者：
Postnova, Olga;Reshetikhin, Nicolai
通讯作者：
Reshetikhin, Nicolai