THE IRREDUCIBLE REPRESENTATIONS OF THE ALTERNATING GROUP WHICH REMAIN IRREDUCIBLE IN CHARACTERISTIC p
5807 - 5855
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Let p be an odd prime, and An the alternating group of degree n. We determine which ordinary irreducible representations of An remain irreducible in characteristic p, verifying the author’s conjecture from [F3]. 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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