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Mat. Zametki, 2012, Volume 92, Issue 3, Pages 323–330 (Mi mz9289)  

This article is cited in 6 scientific papers (total in 7 papers)

On Irreducible Representations of Discrete Heisenberg Groups

S. A. Arnal', A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We prove that the irreducible representations with finite weight of discrete nilpotent groups of class $2$, including the discrete Heisenberg groups, are monomial representations and obtain their classification for the group $\operatorname{Heis}(3,\mathbb Z)$.

Keywords: discrete Heisenberg group, discrete nilpotent group, monomial representation, representation of finite weight

Funding Agency Grant Number
Russian Foundation for Basic Research


DOI: https://doi.org/10.4213/mzm9289

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:3, 295–301

Bibliographic databases:

Document Type: Article
UDC: 512.544.33
Received: 06.12.2011

Citation: S. A. Arnal', A. N. Parshin, “On Irreducible Representations of Discrete Heisenberg Groups”, Mat. Zametki, 92:3 (2012), 323–330; Math. Notes, 92:3 (2012), 295–301

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. R. Ya. Budylin, “Conjugacy classes in discrete Heisenberg groups”, Sb. Math., 205:8 (2014), 1069–1079  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. I. V. Beloshapka, “On representations of a Heisenberg group of matrices with one integer and two real coefficients”, Russian Math. Surveys, 69:5 (2014), 921–923  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. I. V. Beloshapka, “On irreducible representations with finiteweight of a certain discrete nilpotent group”, Russian Math. Surveys, 70:4 (2015), 777–778  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. I. V. Beloshapka, S. O. Gorchinskiy, “Irreducible representations of finitely generated nilpotent groups”, Sb. Math., 207:1 (2016), 41–64  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. 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
    7. Narayanan E.K., Singla P., “On Monomial Representations of Finitely Generated Nilpotent Groups”, Commun. Algebr., 46:6 (2018), 2319–2331  crossref  mathscinet  zmath  isi  scopus
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