Sinead Lyle

From symmetric groups to Ariki-Koike algebras

The Ariki-Koike algebras were defined in 1994 as a simultaneous generalisation of the Hecke algebras of type A and type B. Since the Hecke algebras of type A can be thought of as a deformation of the symmetric group algebra, they include the symmetric group algebra as a special case; indeed, the combinatorics underpinning their representation theory is remarkably similar. For the symmetric groups, there is an important class of modules - the Specht modules - indexed by partitions. For the Ariki-Koike algebras, the Specht modules are indexed by tuples of partitions. In both cases, the blocks are determined by residue classes and may be described using abacus configurations. In this talk, we will look at some of the ways in which results about the symmetric groups have been generalised to Ariki-Koike algebras.