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 (⁺, ⁻). As app...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2023 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2023
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| Online Zugang: | 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 |
| Zitieren: | 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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 |