Abstract
Abstract
Recently, a birational representation of an extended affine Weyl group of
A
2
N
⋊
A
1
1
-type, which gives a higher-order generalization of an
A
4
1
-surface type q-Painlevé equation, was obtained. In this paper, we extend it to a birational representation of an extended affine Weyl group of
A
2
N
⋊
A
1
1
×
A
1
1
-type. Moreover, we provide conjectures on periodic reductions from systems of PΔEs with the CAC property to Painlevé type q-OΔEs.
Funder
Japan Society for the Promotion of Science
Reference64 articles.
1. Higher-order generalizations of the A61 - and A41 -surface type q-Painlevé equations;Nakazono;Phys. Scr.,2023
2. Lattice equations arising from discrete Painlevé systems: II. A41 case;Joshi;J. Phys. A,2016
3. Hypergeometric solutions to the symmetric q-Painlevé equations;Kajiwara;Int. Math. Res. Not. IMRN,2015
4. Hypergeometric τ Functions of the q-Painlevé Systems of Types A41 and (A1+A1′)1;Nakazono;SIGMA Symmetry Integrability Geom. Methods Appl.,2016
5. The q-discrete Painlevé IV equations and their properties;Tamizhmani;Regul. Chaotic Dyn.,2004