Simple singularities and complex reflections (Q2754597)

The Weyl groups of type \(A_k, D_k, E_k\) are realized as the full monodromy groups of simple singularities. The base of the semiuniversal deformation of such a singularity is naturally identified with the complex orbit space of the Weyl group. \textit{V. Goryunov} [Russ. Math. Surv. 54, No. 5, 873-893 (1999); translation from Usp. Mat. Nauk 54, No. 5, 3-24 (1999; Zbl 0971.32010)] has exhibited a way to realize certain complex reflections groups as subgroups of the full monodromy group. Embeddings of complex reflections groups into finite Weyl groups had been encountered in [\textit{T. A. Springer}, Invent. Math. 25, 159-198 (1975; Zbl 0287.20043)]. NEWLINENEWLINENEWLINEThe goal of the reviewed article is to show that these different occurrences are related in a natural way on the base of the notion of a ``Milnor regular'' automorphism of a simple singularity.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00034].