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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