On decomposition matrices for graded algebras

We study the relations between the decomposition matrix of a module over a graded algebra and the decomposition matrix of its restriction to the grading subalgebra. We show that under appropriate hypotheses, if one of the decomposition matrices is “stable unitriangular” then so is the other. A particular case is when one of them is square unitriangular then both are. Using these results, we describe the decomposition matrices of the Hecke algebras of the complex reflection groups G(de,e,n) with respect to the ones of the Ariki–Koike algebras or the decomposition matrices of q-Schur algebras of type Dn with respect to the ones of q-Schur algebras of type Bn.