Open Access
Translator Disclaimer
November 2016 Confluence of general Schlesinger systems and Twistor theory
Hironobu Kimura, Damiran Tseveennamjil
Hiroshima Math. J. 46(3): 289-309 (November 2016). DOI: 10.32917/hmj/1487991623


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.


Download Citation

Hironobu Kimura. Damiran Tseveennamjil. "Confluence of general Schlesinger systems and Twistor theory." Hiroshima Math. J. 46 (3) 289 - 309, November 2016.


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

zbMATH: 1369.34108
MathSciNet: MR3614299
Digital Object Identifier: 10.32917/hmj/1487991623

Primary: 34M55
Secondary: 34M56

Rights: Copyright © 2016 Hiroshima University, Mathematics Program


Vol.46 • No. 3 • November 2016
Back to Top