2007/07/31 by Jun Hu, Andrew Mathas · 7 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Mathematics #Morita therapy #Pure mathematics #Type (biology) #math.CO #math.GR #math.QA #math.RA #math.RT #msc:20C08 #msc:20C30
paper · pdf · doi:10.1515/crelle.2009.022
published in Journal für die reine und angewandte Mathematik (Crelles Journal) 2009(628) (De Gruyter) · Latex file. 21 pages Final published version which corrects a previous error in definition 2.4.
openalex publication_date 2009/01/01 · arxiv created 2010/04/22 · arxiv updated 2010/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove a Morita reduction theorem for the cyclotomic Hecke algebras ℋ r, p, n ( q, Q ) of type G ( r, p, n ) with p > 1 and n ≧ 3. As a consequence, we show that computing the decomposition numbers of ℋ r, p, n ( Q ) reduces to computing the p′-splittable decomposition numbers (see Definition 1.1) of the cyclotomic Hecke algebras ℋ r′, p′, n′ ( Q ′), where 1 ≦ r ′ ≦ r , 1 ≦ n ′ ≦ n , p ′ | p and where the parameters Q ′ are contained in a single ( ɛ′, q )-orbit and ɛ ′ is a primitive p ′th root of unity.