  We give a combinatorial description (including explicit differential-form
bases) for the cohomology groups of the space of n distinct nonzero complex
numbers, with coefficients in rank-one local systems which are of finite
monodromy around the coordinate hyperplanes and trivial monodromy around all
other hyperplanes. In the case where the local system is equivariant for the
symmetric group, we write the cohomology groups as direct sums of inductions of
one-dimensional characters of subgroups. This relies on an equivariant
description of the Orlik-Solomon algebras of full monomial reflection groups
(wreath products of the symmetric group with a cyclic group). The combinatorial
models involved are certain representations of these wreath products which
possess bases indexed by labelled trees.
