Year: 2026
Type: preprint
Abstract: The construction of absolutely irreducible $KG$-modules for a field $K$ and a finite group $G$ is a basic problem in representation theory. For the symmetric group $\operatorname{S}_n$, Gordon James gave an explicit solution using subgroup data associated to a $μ$-tableau $t$ for partitions $μ\vdash n$. Here, we want to investigate in which way James's method can be extended beyond symmetric groups. We identify suitable subgroup data from a finite group and use it to construct a module such that an associated factor module is absolutely irreducible or zero.
Source: arXiv (Cornell University)
Author: Krauß, Nora
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214998607