Author: Andrew Mathas
  School of Mathematics and Statistics F07  +61 2 9351-6058 (Ph.) 
  University of Sydney                      +61 2 9351-4534 (Fax) 
  Sydney, NSW 2006 
  Australia                http://www.maths.usyd.edu.au/u/mathas/ 

Title: Matrix units and generic degrees for the Ariki--Koike algebras.
Status: Submitted.

Abtract:

We compute the generic degrees of the Ariki--Koike algebras by first
constructing a basis of matrix units in the semisimple case. As a
consequence, we also obtain an explicit isomorphism from any
semisimple Ariki--Koike algebra to the group algebra of the
corresponding complex reflection group.