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Affine Yangian and 3-Schur functions
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-09-16 , DOI: 10.1016/j.nuclphysb.2020.115173
Na Wang

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 h1=1,h2=1,h3=0, the 3-Schur functions of 3D Young diagrams become Schur functions of 2D Young diagrams, which is a special case of h1=h,h2=1h,h3=1hh. When h1=h,h2=1h,h3=1hh, 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.



中文翻译:

仿射Yangian和3-Schur函数

3D(3维)杨氏图是2D杨氏图的概括。本文从3D Young图的正交性以及仿射Yangian及其MacMahon表示的性质,获得了与3D Young图相对应的Schur函数,称为3-Schur函数。3-Schur函数是Schur函数的一般化,即H1个=1个H2=-1个H3=0,则3D Young图表的3-Schur函数变成2D Young图表的Schur函数,这是 H1个=HH2=-1个HH3=1个H-H。什么时候H1个=HH2=-1个HH3=1个H-H,则3-Schur函数通过乘以系数变成2D 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是对称的。

更新日期:2020-09-20
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