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