Duality for the general isomonodromy problem

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.