Addendum zu der Arbeit ``Ausgezeichnete Basen von Milnorgittern einfacher Singularitäten'' von E. Voigt. (Addendum to the paper ``Distinguished bases of Milnor lattices of simple singularities'' by E. Voigt) (Q752780)

This short self-contained note is intended as a supplement to the Ph. D. thesis of \textit{E. Voigt} [Bonn Math. Schr. 160 (1985; Zbl 0573.14014); short version in Abh. Math. Semin. Univ. Hamburg 55, 183-190 (1985; Zbl 0576.14004)]. We consider the canonical action of the \(\ell\)-string braid group \(Z_{\ell}\) on the set of (ordered) integral bases (of roots) of a root lattice of type \(A_{\ell}, D_{\ell}, E_ 6, E_ 7, E_ 8\). Generalizing arguments of Looijenga and Deligne, Voigt has shown that the \(Z_{\ell}\)-orbit of such a basis is determined by the product of the reflections corresponding to its vectors. He also determined some of the orbit-lengths. In the note, these calculations are completed, and an error is corrected.