A \(q\)-analogue of the higher order Painlevé type equations with the affine Weyl group symmetry of type \(D\) (Q2816485)

The study of Painlevé equations has led to the one of isomonodromic deformations of Fuchsian systems, of Garnier systems, of systems admitting affine Weyl symmetry of type \(A\) or \(D\) and of matrix Painlevé systems. Later discrete analogs of Painlevé equations have been investigated. The author focuses on higher order differential equations of Painlevé type whose symmetry is descibed by an affine Weyl group of type \(D\) which he calls Sasano systems, and on their \(q\)-difference analogs. To this end he uses a birational realization of Weyl groups as groups of pseudo-isomorphisms of certain algebraic varieties. He studies also continuous limits from \(q\)-difference systems to Sasano systems.