Painlevé equations and complex reflections
Annales de l'Institut Fourier, Volume 53 (2003) no. 4, p. 1009-1022

We will explain how some new algebraic solutions of the sixth Painlevé equation arise from complex reflection groups, thereby extending some results of Hitchin and Dubrovin-- Mazzocco for real reflection groups. The problem of finding explicit formulae for these solutions will be addressed elsewhere.

Nous expliquerons comment de nouvelles solutions algébriques de la sixième équation de Painlevé proviennent des groupes complexes de réflexion, prolongeant les résultats de Hitchin et de Dubrovin--Mazzocco pour les groupes réels de réflexion. Le problème de trouver des formules explicites pour ces solutions sera traité ailleurs.

DOI : https://doi.org/10.5802/aif.1972
Classification:  34M55,  20H15,  55N99
Keywords: Painlevé equations, isomonodromic deformations, non abelian cohomology, complex reflections
@article{AIF_2003__53_4_1009_0,
     author = {Boalch, Philip},
     title = {Painlev\'e equations and complex reflections},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {4},
     year = {2003},
     pages = {1009-1022},
     doi = {10.5802/aif.1972},
     zbl = {1081.34086},
     mrnumber = {2033508},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2003__53_4_1009_0}
}
Boalch, Philip. Painlevé equations and complex reflections. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1009-1022. doi : 10.5802/aif.1972. http://www.numdam.org/item/AIF_2003__53_4_1009_0/

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