Unisingular representations of rank 1 finite simple groups of Lie type

2025/11/07 by Pellegrini, Marco Antonio, Schena, Lorenzo
Mathematics · #20C15 #20C33 #20C34 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2511.05164

openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28

Abstract

A representation Φ: G → GL_n(\mathbbF) 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.

Citations

• Fixed Point Free Actions of Group Elements in Linear Groups and Finite Group Representations
• On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups
• Unisingular representations in arithmetic and Lie theory
• Almost cyclic elements in Weil representations of finite classical groups
• On generators and representations of the sporadic simple groups

Related

• Realizations of Unisingular Representations by Hyperelliptic Jacobians
• Unisingular Specht Modules
• Unisingular representations in arithmetic and Lie theory
• Unisingular subgroups of symplectic group Sp_2n(2) for 2n<250
• Spectra of non-regular elements in irreducible representations of simple algebraic groups