### Abstract

We introduce the concept of ω-lattice, constructed from τ functions of Painlevé systems, on which quad-equations of ABS (Adler-Bobenko-Suris) type appear. In particular, we consider the A_{5}^{(1)}- and A_{6}^{(1)}-surface q-Painlevé systems corresponding affine Weyl group symmetries are of (A_{2} + A_{1})^{(1)} and (A_{1} + A_{1}^{'})^{(1)}-types, respectively.

Original language | English |
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Article number | 092705 |

Number of pages | 26 |

Journal | Journal of Mathematical Physics |

Volume | 56 |

Issue number | 9 |

DOIs | |

Publication status | Published - 30 Sep 2015 |

### Keywords

- dynamical systems
- Euclidean geometries
- complex functions

## Fingerprint Dive into the research topics of 'Lattice equations arising from discrete Painlevé systems. I. (A<sub>2</sub> + A<sub>1</sub>)<sup>(1)</sup> and (A<sub>1</sub> + A<sub>1</sub><sup>'</sup>)<sup>(1)</sup> cases'. Together they form a unique fingerprint.

## Cite this

Joshi, N., Nakazono, N., & Shi, Y. (2015). Lattice equations arising from discrete Painlevé systems. I. (A

_{2}+ A_{1})^{(1)}and (A_{1}+ A_{1}^{'})^{(1)}cases.*Journal of Mathematical Physics*,*56*(9), [092705]. https://doi.org/10.1063/1.4931481