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Representation Theory
Representation Theory
ISSN 1088-4165

 

On the irreducible representations of the alternating group which remain irreducible in characteristic $ p$


Author: Matthew Fayers
Journal: Represent. Theory 14 (2010), 601-626
MSC (2010): Primary 20C30, 20C20; Secondary 05E10
Published electronically: September 1, 2010
MathSciNet review: 2685098
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Abstract: We consider the problem of which ordinary irreducible representations of the alternating group $ \mathfrak{A}_n$ remain irreducible modulo a prime $ p$. We solve this problem for $ p=2$, and present a conjecture for odd $ p$, which we prove in one direction.


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Additional Information

Matthew Fayers
Affiliation: Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom
Email: m.fayers@qmul.ac.uk

DOI: http://dx.doi.org/10.1090/S1088-4165-2010-00390-8
PII: S 1088-4165(2010)00390-8
Received by editor(s): February 15, 2007
Received by editor(s) in revised form: July 3, 2010
Published electronically: September 1, 2010
Additional Notes: Part of this research was undertaken with the support of a Research Fellowship from the Royal Commission for the Exhibition of 1851. The author is very grateful to the Commission for its generous support.
Part of this research was undertaken while the author was visiting the Massachusetts Institute of Technology as a Postdoctoral Fellow. He is very grateful to Professor Richard Stanley for the invitation, and to M.I.T. for its hospitality.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.