Radicals of weight one blocks of Ariki-Koike algebras

2018/08/20 by Yanbo Li, Li, Yanbo, Dashu Xu +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1808.06291

openalex publication_date 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field and q∈ K, q≠ 0, 1. Let \mathcal H_n(q, Q) be an Ariki-Koike algebra, where the cyclotomic parameter Q=(Q₁, Q₂, ⋯, Q_r)∈ K^r with r≥ 2, Q_i=q^a_i, a_i∈ ℤ. For a weight one block B of \mathcal H_n(q, Q), we prove in this paper that rad B=I, where I is the nilpotent ideal constructed for a symmetric cellular algebra in [Radicals of symmetric cellular algebras, Colloq. Math. \bf 133 (2013) 67-83]. We also give some applications of this result.

Related

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• Radicals of symmetric cellular algebras
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