Modified Ariki-Koike algebras and cyclotomic <Emphasis Type="Italic">q</Emphasis>-Schur algebras

The modified Ariki-Koike algebra is a variation of the original Ariki-Koike algebra over an integral domain R. When R is a rational function field over the independent parameters, But for general R, is not isomorphic to , and has a simpler structure than . In this paper, we construct a cellular basis of which has a similar property as the cellular basis of introduced by Dipper-James-Mathas. By comparing these two cellular bases, we obtain some estimate on the decomposition numbers of in terms of the decomposition numbers of . We also prove the integral form of the Schur-Weyl reciprocity between a certain quantum algebra U_q and on the tensor space