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The Quarterly Journal of Mathematics Advance Access published online on December 6, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham024
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

LABELLING THE CHARACTER TABLES OF SYMMETRIC AND ALTERNATING GROUPS

Mark Wildon

Mathematics Department, University of Wales, Swansea SA2 8PP

Email: m.j.wildon{at}swansea.ac.uk


  Abstract

Let X be a character table of the symmetric group Sn. It is shown that unless n = 4 or n = 6, there is a unique way to assign partitions of n to the rows and columns of X so that for all {lambda} and {nu}, X{lambda}{nu} is equal to {chi}{lambda}({nu}), the value of the irreducible character of Sn labelled by {lambda} on elements of cycle type {nu}. Analogous results are proved for alternating groups, and for the Brauer character tables of symmetric and alternating groups.


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