论文标题
$ {\ mathfrak {gl}}}（1）$的3D玻色子，3杰克多项式和仿射Yangian $
3D Bosons, 3-Jack polynomials and affine Yangian of ${\mathfrak{gl}}(1)$
论文作者
论文摘要
3D（3维）年轻图是2D年轻图的概括。在本文中，我们考虑3D玻色子和3杰克多项式。我们将三个参数$ h_1，h_2，h_3 $分别与$ y，x，z $轴相关联。 3个杰克多项式是$ p_ {n，j}的多项式， n \ geq j $具有$ \ mathbb c（H_1，H_2，H_3）$中的系数，这是Schur函数的概括，插孔多项式对3D情况。与Schur函数类似，三杰克多项式也可以由顶点算子和Pieri公式确定。
3D (3 dimensional) Young diagrams are a generalization of 2D Young diagrams. In this paper, We consider 3D Bosons and 3-Jack polynomials. We associate three parameters $h_1,h_2,h_3$ to $y,x,z$-axis respectively. 3-Jack polynomials are polynomials of $P_{n,j}, n\geq j$ with coefficients in $\mathbb C(h_1,h_2,h_3)$, which are the generalization of Schur functions and Jack polynomials to 3D case. Similar to Schur functions, 3-Jack polynomials can also be determined by the vertex operators and the Pieri formulas.
