This article is cited in 7 papers

Irreducible representations of finitely generated nilpotent groups

I. V. Beloshapka^a, S. O. Gorchinskiy<sup>bc

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^c National Research University "Higher School of Economics" (HSE), Moscow

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.

Keywords: finitely generated nilpotent groups, monomial representations, finite weight representations.

UDC: 512.547

MSC: 43А65

Received: 14.08.2015 and 28.09.2015

DOI: 10.4213/sm8582

 English version: Sbornik: Mathematics, 2016, 207:1, 41–64

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