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

Abstract

For any finite group $G$ and any prime $p$ one can ask which ordinary irreducible representations remain irreducible in characteristic $p$. We answer this question for $p=2$ when $G$ is a proper double cover of the symmetric group. Our techniques involve constructing part of the decomposition matrix for a Rouquier block of a double cover, restricting to subgroups using the Brundan--Kleshchev modular branching rules and comparing the dimensions of irreducible representations via the bar-length formula.

Cited by in corpus (2)

• Irreducible projective representations of the alternating group which remain irreducible in characteristic 2
• Spin characters of the symmetric group which are proportional to linear characters in characteristic 2