Irreducible representations of finitely generated nilpotent groups. (11th March 2016)

• Record Type: Journal Article
• Authors: Beloshapka, I V; Gorchinskiy, S O
• Is Part Of: Sbornik. Volume 207:Number 1(2016)
• Page Start: 41
• Page End: 64
• Publication Date: 2016-03-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM8582
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: We prove that irreducible complex representations of finitely generated nilpotent groups are monomial if and only if they have finite weight, which was conjectured by Parshin. Note that we consider (possibly infinite-dimensional) representations without any topological structure. In addition, we prove that for certain induced representations, irreducibility is implied by Schur irreducibility. Both results are obtained in a more general form for representations over an arbitrary field. Bibliography: 21 titles.