International Mathematics Research Notices

International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm032, 24 pages, doi:10.1093/imrn/rnm032 published on June 22, 2007

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Copyright © The Author 2007. Published by Oxford University Press.

An Extension of James's Conjecture

Matthew Fayers

Queen Mary, University of London, Mile End Road, London E1 4NS, U.K.

Correspondence: Correspondence to be sent to: m.fayers{at}qmul.ac.uk

Let B be a block of an Iwahori–Hecke algebra or q-Schur algebra of the symmetric group. The decomposition matrix for B may be obtained from the decomposition matrix of the corresponding block B' in infinite characteristic by post-multiplying by an adjustment matrix; since (by a deep theorem of Ariki) there is an algorithm for computing the decomposition matrix for B', the hard part of the decomposition number problem for B is to find the adjustment matrix. James's Conjecture suggests a sufficient condition for this adjustment matrix to be the identity matrix. We extend James's Conjecture to give a necessary and sufficient condition, and prove the necessity of our condition.

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Communicated by Andrei Zelevinsky

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions How to cite this article Google Scholar Articles by Fayers, M. Search for Related Content Social Bookmarking          What's this?