论文标题
对称变形的2D/3D Hurwitz-Kontsevich模型和GL的Aggine Yangian（1）
Symmetric deformed 2D/3D Hurwitz-Kontsevich model and affine Yangian of gl(1)
论文作者
论文摘要
由于（$β$ - 成型的）Hurwitz Kontsevich模型对应于$ {\ Mathfrak {gl}}}（1）$的Aggine Yangian的特殊情况。在本文中，我们构建了两个$β$成型的Hurwitz Kontsevich模型的一般案例。我们发现，这两种模型的$ W $ - 操作员可以由发电机$ e_k，\ f_k，ψ_k$ $ {\ mathfrak {\ mathfrak {gl}}}（1）$的Aggine Yangian，nougentates usemant $Y__λ$和3- j jack polynomialss）的eigenstates（ $ {\ mathfrak {gl}}（1）$。然后，我们可以看到，$ W $ - 操作器和特征态对坐标轴的排列对称。
Since the ($β$-deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of ${\mathfrak{gl}}(1)$. In this paper, we construct two general cases of the $β$-deformed Hurwitz Kontsevich model. We find that the $W$-operators of these two models can be represented by the generators $e_k,\ f_k,ψ_k$ of the affine Yangian of ${\mathfrak{gl}}(1)$, and the eigenstates (the symmetric functions $Y_λ$ and 3-Jack polynomials) can be obtained from the 3D Young diagram representation of affine Yangian of ${\mathfrak{gl}}(1)$. Then we can see that the $W$-operators and eigenstates are symmetric about the permutations of coordinate axes.
