Simply-laced isomonodromy systems

Understand

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.