For any finite group G and any prime p, it is interesting to ask which ordinary irreducible representations remain irreducible modulo p. For the symmetric and alternating groups this problem was solved several years ago. Here we look at projective representations of symmetric groups, or equivalently representations of double covers of symmetric groups, focussing on characteristic 2 (which behaves very differently from odd characteristic). I'll give the classification of which irreducibles remain irreducible in characteristic 2, and describe some of the methods used in the proof. I'll assume some basic knowledge of representation theory, but I'll introduce projective representations and double covers from scratch.
Irreducible projective representations of symmetric groups which remain irreducible in characteristic 2
Matthew Fayers (QMUL)
Mon, 27/11/2017 - 16:30