Painlevé equations and complex reflections
[Équations de Painlevé et réflexions complexes]
Boalch, Philip
Annales de l'Institut Fourier, Tome 53 (2003), p. 1009-1022 / Harvested from Numdam
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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.

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.

Publié le : 2003-01-01
DOI : https://doi.org/10.5802/aif.1972
Classification:  34M55,  20H15,  55N99
Mots clés: équations de Painlevé, déformations isomonodromiques, cohomologie non abélienne, réflections complexes 
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     title = {Painlev\'e equations and complex reflections},
     journal = {Annales de l'Institut Fourier},
     volume = {53},
     year = {2003},
     pages = {1009-1022},
     doi = {10.5802/aif.1972},
     mrnumber = {2033508},
     zbl = {1081.34086},
     language = {en},
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Boalch, Philip. Painlevé equations and complex reflections. Annales de l'Institut Fourier, Tome 53 (2003) pp. 1009-1022. doi : 10.5802/aif.1972. http://gdmltest.u-ga.fr/item/AIF_2003__53_4_1009_0/

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