Graded decomposition numbers of Ariki–Koike algebras for blocks of small weight

We present some blocks of Ariki–Koike algebras Hn,rHn,r where the decomposition matrices are independent of the characteristic of the underlying field. We complete the description of the graded decomposition numbers for blocks of Ariki–Koike algebras of weight at most two, which consists in analysing the indecomposable core blocks at level r=3r=3, and give a closed formula for the decomposition numbers in this case.