论文标题
杰克多项式，$ \ hbar $依赖的kp层次结构和$ {\ mathfrak {gl}}}（1）$
Jack polynomials, $\hbar$-dependent KP hierarchy and affine Yangian of ${\mathfrak{gl}}(1)$
论文作者
论文摘要
在本文中，我们讨论了杰克多项式，$ \ hbar $依赖的kp层次结构和$ {\ mathfrak {gl}}}（1）$的Aggine Yangian。我们发现$α= \ hbar^2 $和$ h_1 = \ hbar，\ h_2 = - \ hbar^{ - 1} $，其中$α$是jack多项式中的参数，而$ h_1，\ h_2 $是$ hangian yangian yangian of $ yangian of $ {然后，插孔多项式中的顶点操作员与$ \ hbar $ -KP层次结构中的顶点运算符相同，并且可以使用插孔多项式来描述$ \ hbar $ -KP层次结构的tau函数。
In this paper, we discuss the relations between the Jack polynomials, $\hbar$-dependent KP hierarchy and affine Yangian of ${\mathfrak{gl}}(1)$. We find that $α=\hbar^2$ and $h_1=\hbar, \ h_2=-\hbar^{-1}$, where $α$ is the parameter in Jack polynomials, and $h_1,\ h_2$ are the parameters in affine Yangian of ${\mathfrak{gl}}(1)$. Then the vertex operators which are in Jack polynomials are the same with that in $\hbar$-KP hierarchy, and the Jack polynomials can be used to describe the tau functions of the $\hbar$-KP hierarchy.
