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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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On the irreducible representations of the alternating group which remain irreducible in characteristic $p$
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by Matthew Fayers PDF
Represent. Theory 14 (2010), 601-626 Request permission

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
  • 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.
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 14 (2010), 601-626
  • MSC (2010): Primary 20C30, 20C20; Secondary 05E10
  • DOI: https://doi.org/10.1090/S1088-4165-2010-00390-8
  • MathSciNet review: 2685098