Confluent KZ

J. Phys. A: Math. Theor. 41 (2 May 2008) 175205 (14pp) doi: 10.1088/1751-8113/41/17/175205

Remarks on the confluent KZ equation for $\mathfrak{sl}_2$ and quantum Painlevé equations

M Jimbo¹, H Nagoya² and J Sun¹
¹ Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan
² Department of Mathematics, School of Fundamental Science and Technology, Keio University, 3-14-1, Hiyoshi, MinatoKita, Yokohama, Kanagawa, 223-8522 Japan
E-mail: jimbomic@ms.u-tokyo.ac.jp, nagoya@math.keio.ac.jp and sunjuan@ms.u-tokyo.ac.jp

Abstract. For the Lie algebra $\mathfrak{sl}_2$ , we give an explicit form of an irregular-singular version of the KZ equation. In the simplest non-trivial cases these KZ equations reproduce the quantum Painlevé equations $\QPII$ – $\QPV$ possessing affine Weyl group symmetry, found previously by one of the authors.

PACS numbers: 02.30.Hq, 02.20.Sv, 02.30.Ik

Print publication: Issue 17 (2 May 2008)
Received 3 February 2008
Published 15 April 2008

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Remarks on the confluent KZ equation for and quantum Painlevé equations

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Remarks on the confluent KZ equation for $\mathfrak{sl}_2$ and quantum Painlevé equations