Spin characters of the symmetric group which are proportional to linear characters in characteristic 2
Year: 2025
Type: article
Abstract: For a finite group, it is interesting to determine when two ordinary irreducible representations have the same p -modular reduction; that is, when two rows of the decomposition matrix in characteristic p are equal, or equivalently when the corresponding p -modular Brauer characters are the same. We complete this task for the double covers of the symmetric group when p = 2 , by determining when the 2 -modular reduction of an irreducible spin representation coincides with a 2 -modular Specht module. In fact, we obtain a more general result: we determine when an irreducible spin representation has 2 -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.
Source: Annals of representation theory
DOI: 10.5802/art.21
Authors: Matthew Fayers, Eoghan McDowell
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408165667