A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$

Abstract

Recently a certain $q$-Painlevé type system has been obtained from a reduction of the $q$-Garnier system. In this paper it is shown that the $q$-Painlevé type system is associated with another realization of the affine Weyl group symmetry of type $E_7^{(1)}$ and is different from the well-known $q$-Painlevé system of type $E_7^{(1)}$ from the point of view of evolution directions. We also study a connection between the $q$-Painlevé type system and the $q$-Painlevé system of type $E_7^{(1)}$. Furthermore determinant formulas of particular solutions for the $q$-Painlevé type system are constructed in terms of the terminating $q$-hypergeometric function.

References in corpus (6)

• Lax forms of the $q$-Painlevé equations
• A Lax Formalism for the Elliptic Difference Painlevé Equation
• Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$
• Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E^{(1)}_n
• An Elliptic Garnier System from Interpolation
• Padé interpolation for elliptic Painlevé equation