On the Milnor monodromy of the irreducible complex reflection arrangements

TL;DR

This paper determines the monodromy action on the first cohomology of the Milnor fiber for hyperplane arrangements linked to irreducible complex reflection groups, building on recent and previous mathematical results.

Contribution

It provides a detailed analysis of the Milnor monodromy for a class of hyperplane arrangements associated with irreducible complex reflection groups, extending prior work with new refinements.

Findings

Explicit description of monodromy action on H^1 of Milnor fibers

Application of recent results by Macinic, Papadima, and Popescu

Refinement of earlier constructions for better understanding

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 $G$.