The symplectic and twistor geometry of the general isomonodromic deformation problem
Exactly Solvable and Integrable Systems
2009-10-31 v1
Abstract
Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X can be obtained by embedding X in a twistor space Z on which sl(n,C) acts. When a certain obstruction vanishes, the isomonodromic deformations are given by deforming X in Z. This is related to a description of the deformations in terms of Hamiltonian flows on a symplectic manifold constructed from affine orbits in the dual Lie algebra of a loop group.
Keywords
Cite
@article{arxiv.nlin/0007024,
title = {The symplectic and twistor geometry of the general isomonodromic deformation problem},
author = {N. M. J. Woodhouse},
journal= {arXiv preprint arXiv:nlin/0007024},
year = {2009}
}
Comments
35 pages, LATEX