An algorithm for the computation of the decomposition matrices for Ariki-Koike algebras

We give a purely combinatorial algorithm for the computation of the decomposition matrices for Ariki-Koike algebras when the parameters are powers of the same root of unity. It generalizes the LLT algorithm

Crystal graphs of higher level q-deformed Fock spaces, Lusztig a-values and Ariki-Koike algebras

We show that the different labelings of the crystal graph for irreducible highest weight $\mathcal{U}\_q (\hat{\mathfrak{sl}}\_e)$-modules lead to different labelings of the simple modules for non semisimple Ariki-Koike algebras by using Lusztig $a$-values

JMMO Fock space and Geck-Rouquier classification of simple modules for Hecke algebras

This paper is a survey on the representation theory of Hecke algebras, Ariki-Koike algebras and connections with quantum group