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arXiv · 2003.07713

Irreducible projective representations of the alternating group which remain irreducible in characteristic 2

Matthew Fayers
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Abstract

For any finite group G it is an interesting question to ask which ordinary irreducible representations of G remain irreducible in a given characteristic p. We answer this question for p=2 when G is the proper double cover of the alternating group. As a key ingredient in the proof, we prove a formula for the decomposition numbers in Rouquier blocks of double covers of symmetric groups, in terms of Schur P-functions.

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Matthew Fayers. 2020-03-17. Irreducible projective representations of the alternating group which remain irreducible in characteristic 2. https://doi.org/10.1016/j.aim.2020.107340

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