Littlewood-Richardson coefficients via Yang-Baxter equation
Littlewood-Richardson coefficients via Yang-Baxter equation
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通过 Yang-Baxter 方程计算 Littlewood-Richardson 系数
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
A. Postnikov
中科院分区：
文献类型：
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作者：
Oleg A. Gleizer;A. Postnikov
本文给出了量子粒子系统中Littlewood-Richardson系数的一种解释。我们的方法是基于一定的散射矩阵，满足杨巴克斯特型方程。相应的参数的分段线性变换给出了四面体方程的解。这些变换映射自然地与量子包络代数Uq（sln）上的模的对偶标准基有关。我们的建设的副产品是一个明确的描述Kashiwara的参数化的对偶规范基地。这解决了Berenstien和Zelevinsky提出的问题。我们提出了一个图形解释的散射矩阵的网络功能，这是相关的蜂窝克努森和陶。本文的目的是进一步研究一般线性群GL（N）的多项式表示的Grothendieck环KN。设Vλ是GL（N）的最大权λ的不可约表示，Grothendieck环在不可约表示基上的结构常数c ν由下式给出：
This paper presents an interpretation for the Littlewood-Richardson coefficients in terms of a system of quantum particles. Our approach is based on a certain scattering matrix that satisfies a Yang-Baxter-type equation. The corresponding piecewise-linear transformations of parameters give a solution to the tetrahedron equation. These transformation maps are naturally related to the dual canonical bases for modules over the quantum enveloping algebra Uq(sln). A byproduct of our construction is an explicit description for Kashiwara’s parametrizations of dual canonical bases. This solves a problem posed by Berenstien and Zelevinsky. We present a graphical interpretation of the scattering matrices in terms of web functions, which are related to honeycombs of Knutson and Tao. The aim of this paper is to further investigate the Grothendieck ring KN of polynomial representations of the general linear group GL(N). Let Vλ be the irreducible representation of GL(N) with highest weight λ.The structure constants c ν of the Grothendieck ring in the basis of irreducible representations are given by