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 ( ⁺, ⁻...

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Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2023
Автори: Wang, Zhiyuan, Yang, Chenglang
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2023
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
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.
ISSN:1815-0659