Irreducible representations of the alternating group in odd characteristic
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- Proc. Amer. Math. Soc. 125 (1997), 375-380 Request permission
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
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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
- MR Author ID: 360279
- Email: ford@math.washington.edu, bjf6@po.cwru.edu
- 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
- © Copyright 1997 American Mathematical Society
- 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