Weights of multipartitions and representations of Ariki–Koike algebras

We consider representations of the Ariki–Koike algebra, a q-deformation of the group algebra of the complex reflection group Cr≀Sn. The representations of this algebra are naturally indexed by multipartitions of n, and for each multipartition λ we define a non-negative integer called the weight of λ. We prove some basic properties of this weight function, and examine blocks of small weight.