论文标题
2d Toda晶格层次结构的对角线tau函数，连接$（n，m）$ - 点功能和双hurwitz编号
Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers
论文作者
论文摘要
我们为连接的$（n，m）$ - 点函数提供了一个明确的公式，与任意的对角线tau函数$τ_f（\ boldsymbol {t boldsymbol {t}^+，\ boldsymbol {t}^ - ）$使用菲尔米计算的2d toda lattice comportation和boson-boson-ioncon-ioncon-然后，对于固定的$ \ boldsymbol {t}^ - $，我们计算$τ_f（\ boldsymbol {t}^+，\ boldsymbol {t}^ - ）$的kp-affine坐标。作为应用程序，我们提出了一种统一的方法，用于计算各种类型的连接的双Hurwitz号码，包括普通的双Hurwitz号码，完整的$ R $ $ -CYCLE的双Hurwitz号码和混合的双Hurwitz号码。我们还将这种方法应用于$ \ mathbb p^1 $相对于两个点的固定gromov-witten不变性的计算。
We derive an explicit formula for the connected $(n,m)$-point functions associated to an arbitrary diagonal tau-function $τ_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$ of the 2d Toda lattice hierarchy using fermionic computations and the boson-fermion correspondence. Then for fixed $\boldsymbol{t}^-$, we compute the KP-affine coordinates of $τ_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$. As applications, we present a unified approach to compute various types of connected double Hurwitz numbers, including the ordinary double Hurwitz numbers, the double Hurwitz numbers with completed $r$-cycles, and the mixed double Hurwitz numbers. We also apply this method to the computation of the stationary Gromov-Witten invariants of $\mathbb P^1$ relative to two points.
