Double points and image of reflection maps

A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is a hypersurface, we obtain explicit equations for the double point space and for the image as well. In the case of surfaces in ${\text{C}}^3$, this gives a very efficient method to compute the Milnor number and delta invariant of the double point curve.