Rouquier blocks |
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Authors: | Gordon James Sinéad Lyle Andrew Mathas |
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Institution: | (1) Department of Mathematics, Imperial College London, SW7 2AZ, United Kingdom;(2) School of Mathematics and Statistics F07, University of Sydney, NSW, 2006, Australia |
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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. |
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Keywords: | 20C08 20C30 05E10 |
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