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Let G be a finite group and ρ:G → (V) a finite dimensional representation of G. We say that ρ is unisingular if (1-ρ(g)) = 0 for all g ∈ G. Building on previous work in {cullinan}, we consider the symmetric groups Sₙ and prove that certain families of Specht modules are always unisingular as well as raise new questions for future study.
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John Cullinan (2024) studied this question.
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