Year: 2025
Type: article
Abstract: Let 𝐺 be a finite group and ρ : G → GL ( V ) \rho\colon G\to\operatorname{GL}(V) a finite-dimensional representation of 𝐺. We say that 𝜌 is unisingular if det ( 1 − ρ ( g ) ) = 0 \det(1-\rho(g))=0 for all g ∈ G g\in G . Building on previous work in [J. Cullinan, Realizations of unisingular representations by hyperelliptic Jacobians, Comm. Algebra 51 (2023), 12, 5297–5312], we consider the symmetric groups S n S_{n} and prove that certain families of Specht modules are always unisingular as well as raise new questions for future study.
Source: Journal of Group Theory
Author: John Cullinan
Institution: Bard College
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408404632