Geodesic
Simply-laced isomonodromy systems
Boalch, Philip1 
1 École Normale Supérieure et CNRS 45 rue d’Ulm, 75005, Paris France
Publications Mathématiques de l'IHÉS, Tome 116 (2012), pp. 1-68

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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 Painlevé equations, and shows where such Kac–Moody Weyl groups and 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 Painlevé systems lying over each of the classical Painlevé equations. This leads to a conjecture about the Hilbert scheme of points on some Hitchin systems.

DOI : 10.1007/s10240-012-0044-8

Boalch, Philip 1

1 École Normale Supérieure et CNRS 45 rue d’Ulm, 75005, Paris France 
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Boalch, Philip. Simply-laced isomonodromy systems. Publications Mathématiques de l'IHÉS, Tome 116 (2012), pp. 1-68. doi: 10.1007/s10240-012-0044-8

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