The irreducible representations of the alternating group which remain irreducible in characteristic p

Matthew Fayers

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arXiv · 1306.1033

The irreducible representations of the alternating group which remain irreducible in characteristic p

Matthew Fayers

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Abstract

Let p be an odd prime, and A_n the alternating group of degree n. We determine which ordinary irreducible representations of A_n remain irreducible in characteristic p, verifying the author's conjecture from [Represent. Theory 14, 601-626]. Given the preparatory work done in [op. cit.], 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.

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Matthew Fayers. 2013-06-05. The irreducible representations of the alternating group which remain irreducible in characteristic p. https://arxiv.org/abs/1306.1033

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