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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Irreducible representations
of the alternating group in odd characteristic


Author: Ben Ford
Journal: Proc. Amer. Math. Soc. 125 (1997), 375-380
MSC (1991): Primary 20C20, 20C30
MathSciNet review: 1353385
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Abstract: We use the recently-proved conjecture of Mullineux to determine which modular irreducible representations of the symmetric group $\Sigma _n$ split on restriction to $A_n$, and which remain irreducible (everything taking place over a splitting field for $A_n$ of characteristic $p>2$). An indexing of the absolutely irreducible representations of $A_n$ is thus obtained. A modular analogue of the Frobenius symbol for a partition is introduced, which makes the Mullineux map somewhat more intuitive.


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Additional Information

Ben Ford
Affiliation: Department of Mathematics, University of Washington, Box 354350 Seattle, Washington 98195-4350
Address at time of publication: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Email: ford@math.washington.edu, bjf6@po.cwru.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03621-6
PII: S 0002-9939(97)03621-6
Received by editor(s): August 28, 1995
Additional Notes: Supported in part by the NSA
Thanks to Jens C. Jantzen for suggesting this question
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society