Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers
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Published:2023-11-04
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Volume:
Page:
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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language:
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Short-container-title:SIGMA
Author:
Wang Zhiyuan, ,Yang Chenglang,
Abstract
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
Geometry and Topology,Mathematical Physics,Analysis
Cited by
1 articles.
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