# Simply-laced isomonodromy systems

@article{Boalch2011SimplylacedIS,
title={Simply-laced isomonodromy systems},
author={Philip P. Boalch},
journal={Publications math{\'e}matiques de l'IH{\'E}S},
year={2011},
volume={116},
pages={1-68}
}
• P. Boalch
• Published 5 July 2011
• Mathematics
• Publications mathématiques de l'IHÉS
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 Painlev…
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In this paper we determine the motivic class---in particular, the weight polynomial and conjecturally the Poincar\'e polynomial---of the open de Rham space, defined and studied by Boalch, of certain
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We study non-abelian systems of Painlev´e type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in the sense of the
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