From Toda Hierarchy to KP Hierarchy
Using the matrix-resolvent method and a formula of the second-named author on the -point function for a KP tau-function, we show that the tau-function of an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We then generalize this result to tau-functions for the extended Toda hi...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214170 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | From Toda Hierarchy to KP Hierarchy. Di Yang and Jian Zhou. SIGMA 21 (2025), 068, 25 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Using the matrix-resolvent method and a formula of the second-named author on the -point function for a KP tau-function, we show that the tau-function of an arbitrary solution to the Toda lattice hierarchy is a KP tau-function. We then generalize this result to tau-functions for the extended Toda hierarchy (ETH) by developing the matrix-resolvent method for the ETH. As an example, the partition function of Gromov-Witten invariants of the complex projective line is a KP tau-function, and an application to irreducible representations of the symmetric group is obtained.
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| ISSN: | 1815-0659 |