CFT approach to the q-Painlevé VI equation. Issue 1 (15th September 2017) - Jimbo, M.
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