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

• Record Type: Journal Article
• Authors: Jimbo, M.; Nagoya, H.; Sakai, H.
• Is Part Of: Journal of integrable systems. Volume 2:Issue 1(2017)
• Publication Date: 2017-09-15
• Subjects: isomonodromy deformation -- q Painleve equation -- conformal field theory; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyx009
• Languages: English
• ISSNs: 2058-5985

Abstract

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