Let denote the symmetric group on letters and be the Iwahori-Hecke algebra corresponding to . Let be the complex reflection group . Let be a field. Suppose that are elements of , with non-zero. The Ariki-Koike algebra is defined to be the unital associative -algebra with presentation
Ariki gave a necessary and sufficient criterion in terms of the parameters for to be semi-simple, and described the simple modules in this case. These are indexed by multipartitions of with components.
The purpose of this paper is to provide further generalization of the combinatorics of to that of by introducing a notion of ‘weight’ for multipartitions. For each multipartition the author defines a non-negative integer called the weight of . The author proves some basic properties of this weight function, and examines blocks of small weight.