## Hiroshima Mathematical Journal

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

### Confluence of general Schlesinger systems and Twistor theory

Hironobu Kimura and Damiran Tseveennamjil

#### Abstract

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

**Source**

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

**Dates**

Received: 1 October 2015

Revised: 5 July 2016

First available in Project Euclid: 25 February 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1487991623

**Digital Object Identifier**

doi:10.32917/hmj/1487991623

**Mathematical Reviews number (MathSciNet)**

MR3614299

**Zentralblatt MATH identifier**

1369.34108

**Subjects**

Primary: 34M55: Painlevé and other special equations; classification, hierarchies;

Secondary: 34M56: Isomonodromic deformations

**Keywords**

Isomonodromic deformation Twistor theory Confluence

#### Citation

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