Core blocks of Ariki-Koike algebras

Abstract

We examine blocks of the Ariki-Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori-Hecke algebra of type A. We identify a particular type of combinatorial block, which we call a core block, which may be viewed as an analogue of a simple block of the Iwahori-Hecke algebra. We give equivalent characterisations of core blocks and examine their basic combinatorics. © 2006 Springer Science+Business Media, LLC.