Geometric Reductions of ABS equations on an n-cube to discrete Painlevé systems

Nalini Joshi; Nobutaka Nakazono; Yang Shi

doi:10.1088/1751-8113/47/50/505201

Geometric Reductions of ABS equations on an n-cube to discrete Painlevé systems

Nalini Joshi
, Nobutaka Nakazono
, Yang Shi

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

In this paper, we show how to relate n-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlevé equations. We here focus on the reduction from the four-dimensional cube to the q-discrete third Painlevé equation, which is a dynamical system on a rational surface of type A ₅ ⁽¹⁾ with the extended affine Weyl group W̃ ((A ₂ + A ₁ ) ⁽¹⁾ ). We provide general theorems to show that this reduction also extends to other discrete Painlevé equations at least of type A.

Original language	English
Article number	505201
Pages (from-to)	505201-505216
Number of pages	16
Journal	Journal of Physics. A: Mathematical and Theoretical
Volume	47
Issue number	50
DOIs	https://doi.org/10.1088/1751-8113/47/50/505201
Publication status	Published - 25 Nov 2014
Externally published	Yes

Keywords

geometric reductionPACS numbers: 02.30.Ik, 02.20.Qs
discrete Painlevé equations
ABS equations
Geometric reduction
Discrete Painlevé equations

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title = "Geometric Reductions of ABS equations on an n-cube to discrete Painlev{\'e} systems",

abstract = " In this paper, we show how to relate n-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlev{\'e} equations. We here focus on the reduction from the four-dimensional cube to the q-discrete third Painlev{\'e} equation, which is a dynamical system on a rational surface of type A 5 (1) with the extended affine Weyl group {\~W} ((A 2 + A 1 ) (1) ). We provide general theorems to show that this reduction also extends to other discrete Painlev{\'e} equations at least of type A. ",

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author = "Nalini Joshi and Nobutaka Nakazono and Yang Shi",

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T1 - Geometric Reductions of ABS equations on an n-cube to discrete Painlevé systems

AU - Joshi, Nalini

AU - Nakazono, Nobutaka

AU - Shi, Yang

PY - 2014/11/25

Y1 - 2014/11/25

N2 - In this paper, we show how to relate n-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlevé equations. We here focus on the reduction from the four-dimensional cube to the q-discrete third Painlevé equation, which is a dynamical system on a rational surface of type A 5 (1) with the extended affine Weyl group W̃ ((A 2 + A 1 ) (1) ). We provide general theorems to show that this reduction also extends to other discrete Painlevé equations at least of type A.

AB - In this paper, we show how to relate n-dimensional cubes on which ABS equations hold to the symmetry groups of discrete Painlevé equations. We here focus on the reduction from the four-dimensional cube to the q-discrete third Painlevé equation, which is a dynamical system on a rational surface of type A 5 (1) with the extended affine Weyl group W̃ ((A 2 + A 1 ) (1) ). We provide general theorems to show that this reduction also extends to other discrete Painlevé equations at least of type A.

KW - geometric reductionPACS numbers: 02.30.Ik, 02.20.Qs

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KW - ABS equations

KW - Geometric reduction

KW - Discrete Painlevé equations

UR - http://purl.org/au-research/grants/ARC/DP130100967

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JF - Journal of Physics. A: Mathematical and Theoretical

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ER -

Geometric Reductions of ABS equations on an n-cube to discrete Painlevé systems

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