Simply-laced isomonodromy systems
Classical Analysis and ODEs
2012-10-09 v2 Symplectic Geometry
Exactly Solvable and Integrable Systems
Abstract
A new class of isomonodromy equations will be introduced and shown to admit Kac-Moody Weyl group symmetries. This puts into a general context some results of Okamoto on the 4th, 5th and 6th Painleve equations, and shows where such Kac-Moody root systems occur "in nature". A key point is that one may go beyond the class of affine Kac-Moody root systems. As examples, by considering certain hyperbolic Kac-Moody Dynkin diagrams, we find there is a sequence of higher order Painleve systems lying over each of the classical Painleve equations. This leads to a conjecture about the Hilbert scheme of points on some Hitchin systems.
Cite
@article{arxiv.1107.0874,
title = {Simply-laced isomonodromy systems},
author = {Philip Boalch},
journal= {arXiv preprint arXiv:1107.0874},
year = {2012}
}
Comments
68 pages, lots of figures. Final version, to appear in Pub. Math. IHES