Representation theory of the 0-Ariki-Koike-Shoji algebras

F. Hivert, J. -C. Novelli, J. -Y. Thibon

Published 2004-07-13Version 1

We investigate the representation theory of certain specializations of the Ariki-Koike algebras, obtained by setting $q=0$ in a suitably normalized version of Shoji's presentation. We classify the simple and projective modules, and describe restrictions, induction products, Cartan invariants and decomposition matrices. This allows us to identify the Grothendieck rings of the towers of algebras in terms of certain graded Hopf algebras known as the Mantaci-Reutenauer descent algebras, and Poirier Quasi-symmetric functions.