Folding transformations for q-Painleve equations

Abstract

Folding transformation of the Painlevé equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painlevé equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the $q$-difference Painlevé equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painlevé equations through rational surfaces.

91 pages, 200+ figures

References in corpus (2)

• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• CFT approach to the $q$-Painlevé VI equation