On the A-D-E classification of the simple singularities of functions (Q1357494)

The author gives a classification of simple hypersurface singularities by the classification of irreducible Weyl groups not using the normal forms. He proves: For any singularity the following conditions are equivalent: (1) the singularity is simple; (2) the singularity is elliptic; (3) the monodromy group of the singularity is finite; (4) the monodromy group of the singularity is isomorphic to a Weyl group of type \(A_K\), \(D_K\), \(E_6\), \(E_7\), \(E_8\); (5) the mixed Hodge structure in the vanishing cohomologies of the singularity is trivial; (6) the length of the spectrum of the singularity is less than one. Furthermore, if two simple singularities have isomorphic monodromy groups then they are stably equivalent.