On the Milnor monodromy of the irreducible complex reflection arrangements

Abstract

Using recent results by A. Macinic, S. Papadima and R. Popescu, and a refinement of an older construction of ours, we determine the monodromy action on $H^1(F(G),C)$, where $F(G)$ denotes the Milnor fiber of a hyperplane arrangement associated to an irreducible complex reflection group $G$.

v2. We add the statement for the reflection arrangement associated to the exceptional group $G_{31}$ and send to our preprint arXiv: 1606.06615 for a proof along completely different lines