On the Primitive Irreducible Representations of Finitely Generated Linear Groups of Finite Rank

2021/04/30 by Tushev, A. V.
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2104.14768

Abstract

In the paper we study finitely generated linear groups of finite rank which have faithful irreducible primitive representations over a field of characteristic zero. We prove that if an infinite finitely generated linear group G of finite rank has a faithful irreducible primitive representation over a field of characteristic zero then the FC-center Δ(G) of G is infinite.

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• Primitive irreducible representations of finitely generated nilpotent groups
• Irreducible representations of certain nilpotent groups of finite rank
• On infinite groups admitting a faithful irreducible representation
• On the irreducible representations of soluble groups of finite rank
• Groups having a faithful irreducible representation