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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | 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 |
| Цитувати: | From Toda Hierarchy to KP Hierarchy. Di Yang and Jian Zhou. SIGMA 21 (2025), 068, 25 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862733336653332480 |
|---|---|
| author | Yang, Di Zhou, Jian |
| author_facet | Yang, Di Zhou, Jian |
| citation_txt | From Toda Hierarchy to KP Hierarchy. Di Yang and Jian Zhou. SIGMA 21 (2025), 068, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T19:09:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214170 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T19:09:32Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yang, Di Zhou, Jian 2026-02-19T16:04:24Z 2025 From Toda Hierarchy to KP Hierarchy. Di Yang and Jian Zhou. SIGMA 21 (2025), 068, 25 pages 1815-0659 2020 Mathematics Subject Classification: 37K10; 05E05; 14N35; 53D45; 05E10 arXiv:2311.06506 https://nasplib.isofts.kiev.ua/handle/123456789/214170 https://doi.org/10.3842/SIGMA.2025.068 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. One of the authors, D.Y., is grateful to Marco Bertola, Boris Dubrovin, and Youjin Zhang for their advice. We thank Don Zagier for several insightful and helpful comments. We also thank the anonymous referees for constructive comments that helped to improve the presentation. The work is supported by NSFC (No. 12371254, No. 11890662) and CAS No. YSBR-032. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications From Toda Hierarchy to KP Hierarchy Article published earlier |
| spellingShingle | From Toda Hierarchy to KP Hierarchy Yang, Di Zhou, Jian |
| title | From Toda Hierarchy to KP Hierarchy |
| title_full | From Toda Hierarchy to KP Hierarchy |
| title_fullStr | From Toda Hierarchy to KP Hierarchy |
| title_full_unstemmed | From Toda Hierarchy to KP Hierarchy |
| title_short | From Toda Hierarchy to KP Hierarchy |
| title_sort | from toda hierarchy to kp hierarchy |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214170 |
| work_keys_str_mv | AT yangdi fromtodahierarchytokphierarchy AT zhoujian fromtodahierarchytokphierarchy |