Radicals of weight one blocks of Ariki-Koike algebras

摘要

LetKbe a field andq is an element of K,q not equal 0,1.LetHn(q,Q)be an Ariki-Koike algebra, where the cyclotomic parameterQ=(Q1,Q2,MIDLINE HORIZONTAL ELLIPSIS,Qr)is an element of Krwithr >= 2,Qi=qai,ai is an element of Z.For a weight one blockBofHn(q,Q),we prove in this article thatradB=I,whereIis 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.