Matrix units and generic degrees for the Ariki–Koike algebras

This paper uses the Murphy basis of the Ariki–Koike algebras to explicitly construct a complete set of primitive idempotents when these algebras are semisimple and q≠1. As a consequence, we obtain an explicit Wedderburn basis for the Ariki–Koike algebras. Finally, we use these idempotents to compute the generic degrees of the Ariki–Koike algebras.