On the Milnor Monodromy of the Exceptional Reflection Arrangement of Type $G_{31}$

Abstract

Combining recent results by A. D. Mačinic et al. [Doc. Math. (Bielefeld) 22, 135–150 (2017; Zbl 1358.14020)] 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.