CFT approach to the q-Painlevé VI equation

Abstract

Iorgov, Lisovyy and Teschner established a connection between isomonodromic deformation of linear differential equations and Liouville conformal field theory at |$c=1$|⁠. In this article, we present a |$q$| analogue of their construction. We show that the general solution of the |$q$|-Painlevé VI equation is a ratio of four tau functions, each of which is given by a combinatorial series arising in the AGT correspondence. We also propose conjectural bilinear equations for the tau functions. Communicated by: Masatoshi Noumi