Painlevé equations and complex reflections
[Équations de Painlevé et réflexions complexes]
Boalch, Philip1
1 Columbia University, Department of Mathematics, 2990 Broadway, New York NY 10027 (USA)
Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 1009-1022.

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.

DOI : 10.5802/aif.1972
Classification : 34M55, 20H15, 55N99
Keywords: Painlevé equations, isomonodromic deformations, non abelian cohomology, complex reflections
Mot clés : équations de Painlevé, déformations isomonodromiques, cohomologie non abélienne, réflections complexes
Boalch, Philip 1

1 Columbia University, Department of Mathematics, 2990 Broadway, New York NY 10027 (USA) 
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Boalch, Philip. Painlevé equations and complex reflections. Annales de l'Institut Fourier, Colloque en l'honneur de Frédéric Pham, Tome 53 (2003) no. 4, pp. 1009-1022. doi : 10.5802/aif.1972. http://www.numdam.org/articles/10.5802/aif.1972/

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