Rouquier blocks

James, Gordon, Lyle, Sinéad 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
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:52
Last Modified: 21 Oct 2019 11:30
URI: https://ueaeprints.uea.ac.uk/id/eprint/20727
DOI: 10.1007/s00209-005-0863-0

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