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Mat. Sb., 2016, Volume 207, Number 1, Pages 45–72 (Mi msb8582)  

This article is cited in 2 scientific papers (total in 2 papers)

Irreducible representations of finitely generated nilpotent groups

I. V. Beloshapkaa, S. O. Gorchinskiybc

a 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00178
14-01-00160
13-01-00622
13-01-12420
Ministry of Education and Science of the Russian Federation MK-5215.2015.1
НШ-2998.2014.1
Dynasty Foundation
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 14-01-00178), the Programme for the Support of Young Candidates of Science (grant no. MK-5215.2015.1) and the Programme for the Support of Leading Scientific Schools of the President of the Russian Federation (grant no. НШ-2998.2014.1). The first author also acknowledges the support by RFBR grants no. 14-01-00160 and no. 13-01-00622. The second author acknowledges the support by RFBR grant no. 13-01-12420, Dmitrii Zimin's “Dynasty” Foundation and by the subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Global Competitiveness Program.


DOI: https://doi.org/10.4213/sm8582

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

Bibliographic databases:

Document Type: Article
UDC: 512.547
MSC: 43А65
Received: 14.08.2015 and 28.09.2015

Citation: I. V. Beloshapka, S. O. Gorchinskiy, “Irreducible representations of finitely generated nilpotent groups”, Mat. Sb., 207:1 (2016), 45–72; Sb. Math., 207:1 (2016), 41–64

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. D. V. Osipov, A. N. Parshin, “Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. E. K. Narayanan, P. Singla, “On monomial representations of finitely generated nilpotent groups”, Comm. Algebr., 46:6 (2018), 2319–2331  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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