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.
|Number of pages||16|
|Journal||Journal of Physics. A. Mathematical and Theoretical|
|Publication status||Published - 25 Nov 2014|
- geometric reductionPACS numbers: 02.30.Ik, 02.20.Qs
- discrete Painlevé equations
- ABS equations