Reflection arrangements and ribbon representations

Ehrenborg and Jung (2011) recently related the order complex for the lattice of d-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 A to all real reflection groups and the complex reflection groups known as Shephard groups.