Equivalence of v-decomposition matrices for blocks of Ariki-Koike algebras

We consider the representation theory of the Ariki-Koike algebra, a q-deformation of the group algebra of the complex reflection group Cr≀Sn. We examine blocks of the Ariki-Koike algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of n whose Specht modules belong to a block B and those of n−δi(B) whose Specht modules belong to the block B′, obtained from B applying a Scopes' equivalence. This bijection gives us an equivalence for the v-decomposition numbers of the Ariki-Koike algebras.