Rouquier blocks

James, Gordon, Lyle, Sinéad ORCID: https://orcid.org/0000-0002-6032-7721 and Mathas, Andrew (2006) Rouquier blocks. Mathematische Zeitschrift, 252 (3). pp. 511-531. ISSN 0025-5874

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Abstract

This paper investigates the Rouquier blocks of the Hecke algebras of the symmetric groups and the Rouquier blocks of the q-Schur algebras. We first give an algorithm for computing the decomposition numbers of these blocks in the ``abelian defect group case'' and then use this algorithm to explicitly compute the decomposition numbers in a Rouquier block. For fields of characteristic zero, or when q=1 these results are known; significantly, our results also hold for fields of positive characteristic with q?1. We also discuss the Rouquier blocks in the ``non–abelian defect group'' case. Finally, we apply these results to show that certain Specht modules are irreducible.

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, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:52
Last Modified:	18 Jun 2026 15:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/20727
DOI:	10.1007/s00209-005-0863-0

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