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An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: Recent Developments

Painlev¥'e systems arising from integrable hierarchies

22nd September 2006

Author: Masatoshi NOUMI (Kobe University)

Abstract

I will give an overview of a class of Lax representations for Painlev¥'e equations and their generalization in terms of Lie algebras. In that context discrete symmetries of Painlev¥'e systems are described by means of birational Weyl group actions. I will also discuss how they are related to integrable hierarchies associated with affine Lie algebras.