二维Toda格结构的对角tau函数，连通$(n,m)$-点函数和双Hurwitz数

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-04 DOI:10.3842/sigma.2023.085

Zhiyuan Wang, Chenglang Yang

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引用次数: 1

摘要

利用费米子计算和玻色子-费米子对应关系，导出了二维Toda晶格层中任意对角线函数$\tau_f(\boldsymbol{t} +，\boldsymbol{t}^-)$所关联的$(n,m)$-点函数的显式公式。然后对于固定的$\boldsymbol{t}^-$，我们计算$\tau_f(\boldsymbol{t}^+，\boldsymbol{t}^-)$的kp仿射坐标。作为应用，我们给出了一种统一的方法来计算各种类型的连通双Hurwitz数，包括普通双Hurwitz数、完整$r$-环的双Hurwitz数和混合双Hurwitz数。我们还将这种方法应用于计算$\mathbb P^1$相对于两点的平稳Gromov-Witten不变量。

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Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers

We derive an explicit formula for the connected $(n,m)$-point functions associated to an arbitrary diagonal tau-function $\tau_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$ 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 $\tau_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$. 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.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.