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
