Finite braid group orbits in Aff(C)-character varieties of the punctured sphere

Gaël Cousin , Delphine Moussard (1)

1 I2M - Institut de Mathématiques de Marseille

We give a complete description of finite braid group orbits in Aff(C)-character varieties of the punctured Riemann sphere. This is performed thanks to a coalescence procedure and to the theory of finite complex reflection groups. We then derive consequences in the theory of differential equations. These concern algebraicity of isomonodromic deformations for reducible rank two logarithmic connections on the sphere, the Riemann-Hilbert problem and Lauricella hypergeometric functions.

Domaines: Topologie géométrique [math.GT]

Gaël Cousin, Delphine Moussard. Finite braid group orbits in Aff(C)-character varieties of the punctured sphere. International Mathematics Research Notices, 2018. ⟨hal-03485377⟩