  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 F_D-type Lauricella hypergeometric functions.
