Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected ( , )-Point Functions, and Double Hurwitz Numbers
We derive an explicit formula for the connected ( , )-point functions associated with an arbitrary diagonal tau-function ( ⁺, ⁻) of the 2d Toda lattice hierarchy using fermionic computations and the boson-fermion correspondence. Then, for fixed ⁻, we compute the KP-affine coordinates of ( ⁺, ⁻...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212046 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected ( , )-Point Functions, and Double Hurwitz Numbers. Zhiyuan Wang and Chenglang Yang. SIGMA 19 (2023), 085, 33 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We derive an explicit formula for the connected ( , )-point functions associated with an arbitrary diagonal tau-function ( ⁺, ⁻) of the 2d Toda lattice hierarchy using fermionic computations and the boson-fermion correspondence. Then, for fixed ⁻, we compute the KP-affine coordinates of ( ⁺, ⁻). 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 -cycles, and the mixed double Hurwitz numbers. We also apply this method to the computation of the stationary Gromov-Witten invariants of ℙ¹ relative to two points.
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| ISSN: | 1815-0659 |