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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
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, 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/20727 |
| DOI: | 10.1007/s00209-005-0863-0 |
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