Rouquier blocks for Ariki–Koike algebras

Abstract

The Rouquier blocks, also known as the RoCK blocks, are important blocks of the symmetric groups algebras and the Hecke algebras of type $A$, with the partitions labelling the Specht modules that belong to these blocks having a particular abacus configuration. We generalise the definition of Rouquier blocks to the Ariki–Koike algebras, where the Specht modules are indexed by multipartitions, and explore the properties of these blocks.