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

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.

Cited by in corpus (2)

• Decomposition numbers for abelian defect RoCK blocks of double covers of symmetric groups
• Spin characters of the symmetric group which are proportional to linear characters in characteristic 2