Scopes equivalence for blocks of Ariki-Koike algebras

Abstract

We obtain necessary and sufficient conditions for a block of an Ariki-Koike algebra to have the property that all its associated multipartitions have no addable node with a given residue. This leads to a classification of Scopes equivalence classes for Ariki-Koike algebras in terms of their pyramid numbers and Scopes vectors, generalising that for level 1 and for core blocks. Our proof is independent of the results of Richards for level 1.