Blocks of affine and cyclotomic Hecke algebras

Lyle, Sinéad ORCID: https://orcid.org/0000-0002-6032-7721 and Mathas, Andrew (2007) Blocks of affine and cyclotomic Hecke algebras. Advances in Mathematics, 216 (2). pp. 854-878.

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:52
Last Modified:	07 Nov 2024 12:34
URI:	https://ueaeprints.uea.ac.uk/id/eprint/20723
DOI:	10.1016/j.aim.2007.06.008

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