Generalized pentagram maps via Q-nets and refactorization mappings
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917866091053056 |
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| author | Wang, Bao |
| author_facet | Wang, Bao |
| contents | We introduce a family of generalizations of the pentagram maps related to $Q$-nets. A specific example is considered, and we find the map can be treated as a refactorization mapping in the Poisson-Lie group of pseudo-difference operators. This method was firstly proposed by Izosimov, and we generalize it to fit our needs. Using this description, we obtain the corresponding Lax form with a spectral parameter and invariant Poisson brackets. Finally, we consider the reduction to $B$-nets and the discrete BKP equation, offering a geometric explanation for the discrete-time Toda equation of BKP type proposed by Hirota. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_08202 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized pentagram maps via Q-nets and refactorization mappings Wang, Bao Exactly Solvable and Integrable Systems Mathematical Physics We introduce a family of generalizations of the pentagram maps related to $Q$-nets. A specific example is considered, and we find the map can be treated as a refactorization mapping in the Poisson-Lie group of pseudo-difference operators. This method was firstly proposed by Izosimov, and we generalize it to fit our needs. Using this description, we obtain the corresponding Lax form with a spectral parameter and invariant Poisson brackets. Finally, we consider the reduction to $B$-nets and the discrete BKP equation, offering a geometric explanation for the discrete-time Toda equation of BKP type proposed by Hirota. |
| title | Generalized pentagram maps via Q-nets and refactorization mappings |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2412.08202 |