Mathematical analysis classifies complex irreducible unisingular representations in rank 1 Lie-type and sporadic groups, advancing finite group character theory.
A representation Φ: G → GLₙ(F) of a finite group G is called unisingular if the matrix $Φ(g)$ admits $1$ as an eigenvalue for any g∈ G. In this paper, we determine all the complex irreducible unisingular representations of the finite simple groups of Lie type of rank $1$ and of the almost simple sporadic groups.
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