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Irreducible Representations of the Alternating Group in Odd Characteristic

We use the recently-proved conjecture of Mullineux to determine which modular irreducible representations of the symmetric group ∑n split on restriction to An, and which remain irreducible (everything taking place over a splitting field for An of characteristic p .2). An indexing of the absolutely irreducible representations of An is thus obtained. A modular analogue of the Frobenius symbol for a partition is introduced, which makes the Mullineux map somewhat more intuitive.

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