On double centralizer properties between quantum groups and Ariki-Koike algebras

In this paper, the double centralizer properties for tensor spaces as bimodules over quantum groups and Ariki-Koike algebras as well as their relations with Shoji's algebra H^h (see [J. Algebra 226 (2000) 818-856]) are studied. We proved that, under the separation condition (see [J. Reine Angew. Math. 513 (1999) 53-69]), the natural homomorphism from the Ariki-Koike algebra to the endomorphism algebra of tensor space as module over quantum group is surjective. We also show that the natural homomorphism from Shoji's algebra H^h to that endomorphism algebra is always surjective, and H^h is actually isomorphic to a direct sum of some matrix algebras over some Hecke algebras of type A.