Duality for the general isomonodromy problem
arXiv:nlin/0601003 · doi:10.1016/j.geomphys.2006.09.009
Abstract
By an extension of Harnad's and Dubrovin's `duality' constructions, the general isomonodromy problem studied by Jimbo, Miwa, and Ueno is equivalent to one in which the linear system of differential equations has a regular singularity at the origin and an irregular singularity at infinity (both resonant). The paper looks at this dual formulation of the problem from two points of view: the symplectic geometry of spaces associated with the loop group of the general linear group, and a generalization of the self-dual Yang-Mills equations.
References in corpus (1)
Cited by in corpus (5)
- Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations
- Middle Convolution and Harnad Duality
- Hamiltonian structure of rational isomonodromic deformation systems
- Description of generalized isomonodromic deformations of rank two linear differential equations using apparent singularities
- Isomonodromic deformations: Confluence, Reduction Quantisation