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arXiv · 2412.08202

Generalized pentagram maps via Q-nets and refactorization mappings

Bao Wang
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Abstract

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.

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Bao Wang. 2024-12-11. Generalized pentagram maps via Q-nets and refactorization mappings. https://arxiv.org/abs/2412.08202

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