An Isaac Newton Institute Workshop

Painleve Equations and Monodromy Problems: Recent Developments

Degeneration and symmetry of the Schlesinger system from the point of view of Twistor theory

Author: Hironobu Kimura (Kumamoto University)

Abstract

Using the idea of Mason and Woodhouse, I will describe the isomonodromic deformation of the linear systems of differential equations on P^1. The deformation equations are defined on the Grassmannian manifold Gr(2,N). Using the method of constructing the confluence process for the general hypergeometric system on the Grassmaniann, we will describe the degeneration (confluence) of the isomonodromic deformation of the above system in a explicit way. Some symmetric property will be also discussed for the degenerated Schlesinger system.