On decomposition numbers of the cyclotomic q-Schur algebras

AbstractLet S(Λ) be the cyclotomic q-Schur algebra associated to the Ariki–Koike algebra H. We construct a certain subalgebra S0(Λ) of S(Λ), and show that it is a standardly based algebra in the sense of Du and Rui. S0(Λ) has a natural quotient S0¯(Λ), which turns out to be a cellular algebra. In the case where the modified Ariki–Koike algebra H♭ is defined, S0¯(Λ) coincides with the cyclotomic q-Schur algebra associated to H♭. In this paper, we discuss a relationship among the decomposition numbers of S(Λ), S0(Λ) and S0¯(Λ). In particular, we show that some important part of the decomposition matrix of S(Λ) coincides with a part of the decomposition matrix of S0¯(Λ)