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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
DOI: https://doi.org/10.1090/S0002-9939-97-03621-6
MathSciNet review: 1353385
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. George E. Andrews, Generalized Frobenius partitions, Mem. Amer. Math. Soc. 49 (1984), no. 301, 1-44. MR 85m:11063
  • 2. George E. Andrews and Jørn B. Olsson, Partition identities with an application to group representation theory, J. Reine Angew. Math. 413 (1991), 198-212. MR 91k:20019
  • 3. Dave Benson, Spin modules for symmetric groups, J. London Math. Soc. (2) 38 (1988), 250-262. MR 89k:20020
  • 4. Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Wiley, New York, 1962. MR 26:2519
  • 5. Ben Ford and Alexander Kleshchev, A proof of the Mullineux conjecture, Math. Z. (to appear).
  • 6. Gordon D. James, The irreducible representations of the symmetric groups, Bull. London Math. Soc. 8 (1976), 229-232. MR 54:5329
  • 7. Gordon D. James and Adalbert Kerber, The representation theory of the symmetric group, Addison-Wesley, London, 1981. MR 83k:20003
  • 8. Glen Mullineux, Bijections of $p$-regular partitions and $p$-modular irreducibles of the symmetric groups, J. London Math. Soc. (2) 20 (1979), 60-66. MR 80j:20016
  • 9. Daniel Edwin Rutherford, Substitutional analysis, Edinburgh University Press, 1948. MR 10:280i

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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: https://doi.org/10.1090/S0002-9939-97-03621-6
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

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