GRADED DECOMPOSITION NUMBERS FOR BLOCKS OF SMALL WEIGHT
We consider some blocks of Ariki-Koike algebras Hn,r where the decomposition matrices are independent of the characteristic of the underlying field. We complete the description of the graded decom- position numbers for blocks of Ariki-Koike algebras of weight at most two, which consists of analysing the indecomposable core blocks at level r = 3, and look in some detail at core blocks in higher levels whose weight graphs are trees. We end with some graded decomposition numbers for such blocks when r = 4.