  We relate the classes of unitary and calibrated representations of cyclotomic
Hecke algebras and, in particular, we show that for the most important
deformation parameters these two classes coincide. We classify these
representations in terms of both multipartition combinatorics and as the points
in the fundamental alcove under the action of an affine Weyl group. Finally, we
cohomologically construct these modules via BGG resolutions.
