On the Milnor monodromy of the exceptional reflection arrangement of type $G_{31}$

Abstract

Combining recent results by A. Macinic, S. Papadima and R. Popescu with a spectral sequence and computer aided computations, we determine the monodromy action on $H^1(F,\mathbb{C})$, where $F$ denotes the Milnor fiber of the hyperplane arrangement associated to the exceptional irreducible complex reflection group $G_{31}$. This completes the description given by the first author of such monodromy operators for all the other irreducible complex reflection groups.

arXiv commentv3. Minor changes in the presentation. Most of the Singular codes used in the paper are available now on the webpage of the first author