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 |
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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 | |
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