Reflection arrangements and ribbon representations

Ehrenborg and Jung (2011) recently related the order complex for the lattice of dd-divisible partitions with the simplicial complex of pointed ordered set partitions   via a homotopy equivalence. The latter has top homology naturally identified as a Specht module. Their work unifies that of Calderbank, Hanlon, Robinson (1986), and Wachs (1996). By focusing on the underlying geometry, we strengthen and extend these results from type AA to all real reflection groups and the complex reflection groups known as Shephard groups.