Radicals of weight one blocks of Ariki–Koike algebras

Abstract

Let K be a field and Let be an Ariki–Koike algebra, where the cyclotomic parameter with For a weight one block B of we prove in this article that where I is the nilpotent ideal constructed for a symmetric cellular algebra [Radicals of symmetric cellular algebras, Colloq. Math. 133 (2013) 67–83]. We also give some applications of this result.