THE IRREDUCIBLE REPRESENTATIONS OF THE ALTERNATING GROUP WHICH REMAIN IRREDUCIBLE IN CHARACTERISTIC p

Let p be an odd prime, and An the alternating group of degree n. We determine which ordinary irreducible representations of U-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.