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Hypergeometric solutions to Schr\"odinger equations for the quantum Painlev\'e equations
We consider Schr\"odinger equations for the quantum Painlev\'e equations. We
present hypergeometric solutions of the Schr\"odinger equations for the quantum
Painlev\'e equations, as particular solutions. We also give a representation
theoretic correspondence between Hamiltonians of the Schr\"odinger equations
for the quantum Painlev\'e equations and those of the KZ equation or the
confluent KZ equations.Comment: 17 pages; Journal of Mathematical Physics (Vol.52, Issue 8) 201
CFT approach to the -Painlev\'e VI equation
Iorgov, Lisovyy, and Teschner established a connection between isomonodromic
deformation of linear differential equations and Liouville conformal field
theory at . In this paper we present a analog of their construction.
We show that the general solution of the -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.Comment: 26 page
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