Generalized pentagram maps via Q-nets and refactorization mappings
arXiv:2412.08202
Abstract
We introduce a family of generalizations of the pentagram maps related to -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 -nets and the discrete BKP equation, offering a geometric explanation for the discrete-time Toda equation of BKP type proposed by Hirota.
30 pages