Regular elements and monodromy of discriminants of finite reflection groups
Let \(G \subseteq GL_n (\mathbb{C})\) be a finite subgroup generated by reflections. For each reflection hyperplane \(H\) of \(G\) let \(\ell_H : \mathbb{C}^n \to \mathbb{C}\) be a linear form defining \(H\) and \(e(H)\) the order of the subgroup of elements of \(G\) which fix \(H\) pointwise. Let \(\delta = \prod_H \ell_H^{e(H)}\) and \(\Delta : \mathbb{C}^n/G \to \mathbb{C}\) the map induced by \(\delta\). Let \(Z(T,G)\) be the zeta function of the local monodromy of \(\Delta\) at 0. This zeta function is calculated case by case for all irreducible finite reflection groups \(G\).
scientific article; zbMATH DE number 792820
scientific article