Hiroshima Mathematical Journal

Confluence of general Schlesinger systems and Twistor theory

Hironobu Kimura and Damiran Tseveennamjil

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We give a description of confluence for the general Schlesinger systems (GSS) from the view point of twistor theory. GSS is a system of nonlinear di¤erential equations on the Grassmannian manifold $G_{2,N}(\mathbf{C}$ which is obtained, for any partition $\lambda$ of $N$, as the integrability condition of a connection $\nabla_\lambda$ on $\mathbf{P}^1\times G_{2,N}$ constructed using the twistor-theoretic point of view and is known to describe isomonodromic deformation of linear differential equations on the projective space $\mathbf{P}^1$. For a pair of partitions $\lambda, \mu$ of $N$ such that m is obtained from $\lambda$ by making two parts into on parts and leaving other parts unchanged, we construct the limit process $\nabla_\lambda\to \nabla_\mu$ and as a result the confluence for GSS.

Article information

Hiroshima Math. J., Volume 46, Number 3 (2016), 289-309.

Received: 1 October 2015
Revised: 5 July 2016
First available in Project Euclid: 25 February 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34M55: Painlevé and other special equations; classification, hierarchies;
Secondary: 34M56: Isomonodromic deformations

Isomonodromic deformation Twistor theory Confluence


Kimura, Hironobu; Tseveennamjil, Damiran. Confluence of general Schlesinger systems and Twistor theory. Hiroshima Math. J. 46 (2016), no. 3, 289--309. doi:10.32917/hmj/1487991623. https://projecteuclid.org/euclid.hmj/1487991623

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