Affine Yangian and 3-Schur functions
Affine Yangian and 3-Schur functions
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DOI：
10.1016/j.nuclphysb.2020.115173
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发表时间：
2020-11
期刊：
影响因子：
--
通讯作者：
Na Wang
中科院分区：
文献类型：
--
作者：
Na Wang
三维杨氏图是二维杨氏图的推广。本文从三维Young图的正交性和仿射Yangian及其MacMahon表示的性质出发，得到了对应于三维Young图的Schur函数，称之为3-Schur函数。3-Schur函数是Schur函数的推广，当h 1= 1，h 2=− 1，h 3= 0时，三维Young图的3-Schur函数变成二维Young图的Schur函数，这是h 1= h，h 2=− 1 h，h 3= 1 h− h的特殊情况。当h1 = h，h2 =− 1 h，h3 = 1 h− h时，3-Schur函数通过乘以一个系数变成二维Young图的Jack对称多项式。我们将看到3-Schur函数关于三个坐标轴对称。
Abstract 3D (3 dimensional) Young diagram is a generalization of 2D Young diagram. In this paper, from the orthogonality of 3D Young diagrams and the properties in affine Yangian and its MacMahon representation, we obtain the Schur functions corresponding to 3D Young diagrams, which are called 3-Schur functions. 3-Schur functions are a generalization of Schur functions in the sense that when h 1= 1, h 2=− 1, h 3= 0, the 3-Schur functions of 3D Young diagrams become Schur functions of 2D Young diagrams, which is a special case of h 1= h, h 2=− 1 h, h 3= 1 h− h. When h 1= h, h 2=− 1 h, h 3= 1 h− h, the 3-Schur functions turn into the Jack symmetric polynomials of 2D Young diagrams by multiplying a coefficient. We will see that 3-Schur functions are symmetric about three coordinate axes.