On an infinite commuting ODE system associated to a simple Lie algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916222697734144 |
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| author | Yang, Di Zhang, Cheng Zhou, Zejun |
| author_facet | Yang, Di Zhang, Cheng Zhou, Zejun |
| contents | Inspired by a recent work of Dubrovin [7], for each simple Lie algebra $\mathfrak{g}$, we introduce an infinite family of pairwise commuting ODEs and define their $τ$-functions. We show that these $τ$-functions can be identified with the $τ$-functions for the Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type. Explicit examples for $\mathfrak{g}=A_1$ and $A_2$ are provided, which are connected to the KdV hierarchy and the Boussinesq hierarchy respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an infinite commuting ODE system associated to a simple Lie algebra Yang, Di Zhang, Cheng Zhou, Zejun Exactly Solvable and Integrable Systems Mathematical Physics Inspired by a recent work of Dubrovin [7], for each simple Lie algebra $\mathfrak{g}$, we introduce an infinite family of pairwise commuting ODEs and define their $τ$-functions. We show that these $τ$-functions can be identified with the $τ$-functions for the Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type. Explicit examples for $\mathfrak{g}=A_1$ and $A_2$ are provided, which are connected to the KdV hierarchy and the Boussinesq hierarchy respectively. |
| title | On an infinite commuting ODE system associated to a simple Lie algebra |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2404.16458 |