On the parametrization of the simple modules for Ariki-Koike algebras at roots of unity

Following the ideas of M.Geck and R.Rouquier in [19], we show that there exists a "canonical basic set" of Specht modules in bijection with the set of simple modules of Ariki-Koike algebras at roots of unity. Moreover, we determine the parametrization of this set and we give the consequences of these results on the representation theory of Ariki-Koike algebras.