From Toda Hierarchy to KP Hierarchy
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909729695989760 |
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| author | Yang, Di Zhou, Jian |
| author_facet | Yang, Di Zhou, Jian |
| contents | Using the matrix-resolvent method and a formula of the second-named author on the $n$-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 on irreducible representations of the symmetric group is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_06506 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From Toda Hierarchy to KP Hierarchy Yang, Di Zhou, Jian Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry Using the matrix-resolvent method and a formula of the second-named author on the $n$-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 on irreducible representations of the symmetric group is obtained. |
| title | From Toda Hierarchy to KP Hierarchy |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry |
| url | https://arxiv.org/abs/2311.06506 |