On decomposition numbers of the cyclotomic q-Schur algebras

Let be the cyclotomic q-Schur algebra associated to the Ariki–Koike algebra . We construct a certain subalgebra of , and show that it is a standardly based algebra in the sense of Du and Rui. has a natural quotient , which turns out to be a cellular algebra. In the case where the modified Ariki–Koike algebra is defined, coincides with the cyclotomic q-Schur algebra associated to . In this paper, we discuss a relationship among the decomposition numbers of , and . In particular, we show that some important part of the decomposition matrix of coincides with a part of the decomposition matrix of .