On the Milnor monodromy of the exceptional reflection arrangement of type G31

Abstract

Combining recent results by A. M\u acinic, S. Papadima and R. Popescu with a spectral sequence and computer aided computations, we determine the monodromy action on $H^1(F,\C)$, 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.