For a finite group, it is interesting to determine when two ordinary irreducible representations have the same -modular reduction; that is, when two rows of the decomposition matrix in characteristic are equal, or equivalently when the corresponding -modular Brauer characters are the same. We complete this task for the double covers of the symmetric group when , by determining when the -modular reduction of an irreducible spin representation coincides with a -modular Specht module. In fact, we obtain a more general result: we determine when an irreducible spin representation has -modular Brauer character proportional to that of a Specht module. In the course of the proof, we use induction and restriction functors to construct a function on generalised characters which has the effect of swapping runners in abacus displays for the labelling partitions.
Revised:
Accepted:
Published online:
Fayers, Matthew 1; McDowell, Eoghan 2
CC-BY 4.0
@article{ART_2025__2_1_37_0,
author = {Fayers, Matthew and McDowell, Eoghan},
title = {Spin characters of the symmetric group which are proportional to linear characters in characteristic $2$},
journal = {Annals of Representation Theory},
pages = {37--83},
publisher = {The Publishers of ART},
volume = {2},
number = {1},
year = {2025},
doi = {10.5802/art.21},
language = {en},
url = {https://art.centre-mersenne.org/articles/10.5802/art.21/}
}
TY - JOUR AU - Fayers, Matthew AU - McDowell, Eoghan TI - Spin characters of the symmetric group which are proportional to linear characters in characteristic $2$ JO - Annals of Representation Theory PY - 2025 SP - 37 EP - 83 VL - 2 IS - 1 PB - The Publishers of ART UR - https://art.centre-mersenne.org/articles/10.5802/art.21/ DO - 10.5802/art.21 LA - en ID - ART_2025__2_1_37_0 ER -
%0 Journal Article %A Fayers, Matthew %A McDowell, Eoghan %T Spin characters of the symmetric group which are proportional to linear characters in characteristic $2$ %J Annals of Representation Theory %D 2025 %P 37-83 %V 2 %N 1 %I The Publishers of ART %U https://art.centre-mersenne.org/articles/10.5802/art.21/ %R 10.5802/art.21 %G en %F ART_2025__2_1_37_0
Fayers, Matthew; McDowell, Eoghan. Spin characters of the symmetric group which are proportional to linear characters in characteristic $2$. Annals of Representation Theory, Volume 2 (2025) no. 1, pp. 37-83. doi : 10.5802/art.21. https://art.centre-mersenne.org/articles/10.5802/art.21/
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