The irreducible representations of the alternating group which remain irreducible in characteristic $p$
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Abstract:
Let $p$ be an odd prime, and $\mathfrak {A}_n$ the alternating group of degree $n$. We determine which ordinary irreducible representations of $\mathfrak {A}_n$ remain irreducible in characteristic $p$, verifying the author’s conjecture from 2010. Given the preparatory work done in 2010, our task is to determine which self-conjugate partitions label Specht modules for the symmetric group in characteristic $p$ having exactly two composition factors. This is accomplished through the use of the Robinson–Brundan–Kleshchev ‘$i$-restriction’ functors, together with known results on decomposition numbers for the symmetric group and additional results on the Mullineux map and homomorphisms between Specht modules.References
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Additional Information
- Matthew Fayers
- Affiliation: School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
- Email: m.fayers@qmul.ac.uk
- Received by editor(s): November 27, 2013
- Received by editor(s) in revised form: July 25, 2014
- Published electronically: December 3, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 5807-5855
- MSC (2010): Primary 20C30, 05E10, 20C20
- DOI: https://doi.org/10.1090/tran/6531
- MathSciNet review: 3458400