Proceedings of Symposia in Pure MathematicsVolume 00 , 19 xx Simple modules of Ariki

Simple modules of Ariki{Koike algebras

On the classification of simple modules for cyclotomic Hecke algebras of type G(m, 1, n) and Kleshchev multipartitions

We give a proof of a conjecture that Kleshchev multipartitions are those partitions which parametrize non-zero simple modules obtained as factor modules of Specht modules by their own radicals.

The representation theory of the Ariki-Koike and cyclotomic q-Schur algebras

The Ariki-Koike algebras were introduced by Ariki and Koike [8] who were interested in them because they are a natural generalization of the Iwahori-Hecke algebras of types A and B. At almost the same time, Broué and Malle [21] attached to each complex reflection group a cyclotomic Hecke algebra which, they conjectured, should play a role in the decomposition of the induced cuspidal representat...

Generalised canonical basic sets for Ariki-Koike algebras

Let H be a non semi-simple Ariki-Koike algebra. According to [19] and [15], there is a generalisation of Lusztig’s a-function which induces a natural combinatorial order (parametrised by a tuple m) on Specht modules. In some cases, Geck and Jacon have proved that this order makes unitriangular the decomposition matrix of H . The algebra H is then said to admit a "canonical basic set". We fully ...

The Number of Simple Modules of the Hecke Algebras of Type G(r; 1; N)