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arXiv · 1706.01940

CFT approach to the $q$-Painlev\'e VI equation

M. Jimbo·H. Nagoya·H. Sakai
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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 paper we present a $q$ analog of their construction. We show that the general solution of the $q$-Painlev\'e 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.

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M. Jimbo, H. Nagoya, H. Sakai. 2017-06-06. CFT approach to the $q$-Painlev\'e VI equation. https://arxiv.org/abs/1706.01940

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