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Blocks of cyclotomic Hecke algebras

2006/07/31 by Sinéad Lyle, Sinead Lyle, Andrew Mathas · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Finite Group Theory Research #math.CO #math.RT #msc:05E10 #msc:20C08 #msc:20C30

paper · pdf · doi:10.1016/j.aim.2007.06.008

published as Adv. Math, Volume 216, Issue 2, 20 December 2007, Pages 854-878 · Final version. To appear in Advances in Mathematics

arxiv created 2007/06/17 · openalex publication_date 2007/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

This paper classifies the blocks of the cyclotomic Hecke algebras of type G(r,1,n) over an arbitrary field. Rather than working with the Hecke algebras directly we work instead with the cyclotomic Schur algebras. The advantage of these algebras is that the cyclotomic Jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic Schur algebras. We obtain an explicit description of the blocks by analyzing the combinatorics of `Jantzen equivalence'. We remark that a proof of the classification of the blocks of the cyclotomic Hecke algebras was announced in 1999. Unfortunately, Cox has discovered that this previous proof is incomplete.

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