Geodesic
Irreducible representations of finitely generated nilpotent groups
Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 41-64

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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.
Keywords: finitely generated nilpotent groups, finite weight representations.
Mots-clés : monomial representations 
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I. V. Beloshapka; S. O. Gorchinskiy. Irreducible representations of finitely generated nilpotent groups. Sbornik. Mathematics, Tome 207 (2016) no. 1, pp. 41-64. http://geodesic.mathdoc.fr/item/SM_2016_207_1_a1/