  We study natural partial normalization spaces of Coxeter arrangements and
discriminants and relate their geometry to representation theory. The
underlying ring structures arise from Dubrovin's Frobenius manifold structure
which is lifted (without unit) to the space of the arrangement. We also
describe an independent approach to these structures via duality of maximal
Cohen--Macaulay fractional ideals. In the process, we find 3rd order
differential relations for the basic invariants of the Coxeter group. Finally,
we show that our partial normalizations give rise to new free divisors.
