A higher-order generalization of an $A_4^{(1)}$-surface type $q$-Painlev\'e equation with $\widetilde{W}\left((A_{2N}\rtimes A_1)^{(1)}\times A_1^{(1)}\right)$ symmetry

Author:

Nobutaka Nakazono

Keyword:

Nonlinear Sciences, Exactly Solvable and Integrable Systems, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics (math-ph)

journal:

date:

2023-12-27 00:00:00

Abstract

In \cite{nakazono2023higerA4A6}, a birational representation of an extended affine Weyl group of $(A_{2N}\rtimes A_1)^{(1)}$-type, which gives a higher-order generalization of an $A_4^{(1)}$-surface type $q$-Painlev\'e equation, was obtained. In this paper, we extend it to a birational representation of an extended affine Weyl group of $(A_{2N}\rtimes A_1)^{(1)}\times A_1^{(1)}$-type. Moreover, we provide conjectures on periodic reductions from systems of P$\Delta$Es with the CAC property to Painlev\'e type $q$-O$\Delta$Es.

PDF: A higher-order generalization of an $A_4^{(1)}$-surface type $q$-Painlev\'e equation with $\widetilde{W}\left((A_{2N}\rtimes A_1)^{(1)}\times A_1^{(1)}\right)$ symmetry.pdf