Painlevé type equations and Hitchin systems

Details Painlevé type equations and Hitchin systems Painlevé type equations and Hitchin systems

1999-01-25

arxiv.org/abs/math-ph/9901019v1

Physics

Mathematical Physics

19 pages, Latex, Contribution in the Proceedings "Integrability: the Seiberg-Witten and Whitham Equations", Edinburgh, Septemb

Scientific paper

In this survey we present the interpretation of isomondromy preserving equations on Riemann surfaces with marked points as reduced Hamiltonian systems. The upstairs space is the space of smooth connections of GL(N) bundles with simple poles in the marked points. We discuss relations of these equations with the Whitham quantization of the Hitchin systems and with the classical limit of the Knizhnik-Zamolodchikov-Bernard equations. The main example is the one-parameter family of Painlev\'{e} VI equation and its multicomponent generalization.

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