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Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1273–1279 (Mi smj2493)  

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

Irreducible representations of subgroups of finite index in Baumslag–Solitar groups

F. A. Dudkinab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We describe all finite-dimensional irreducible linear representations over the field of complex numbers for an arbitrary subgroup of finite index of a Baumslag–Solitar group $BS(p,q)=\langle a,t\mid t^{-1}a^pt=a^q\rangle$ for coprime $p$ and $q$. We find necessary and sufficient conditions for the equivalence of these representations, using only standard facts of linear algebra and the description of subgroups of finite index in Baumslag–Solitar groups.

Keywords: Baumslag–Solitar group, irreducible representation, subgroup of finite index.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1013–1017

Bibliographic databases:

UDC: 512.543+512.547
Received: 13.06.2012
Revised: 16.11.2012

Citation: F. A. Dudkin, “Irreducible representations of subgroups of finite index in Baumslag–Solitar groups”, Sibirsk. Mat. Zh., 54:6 (2013), 1273–1279; Siberian Math. J., 54:6 (2013), 1013–1017

Citation in format AMSBIB
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\paper Irreducible representations of subgroups of finite index in Baumslag--Solitar groups
\jour Sibirsk. Mat. Zh.
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\vol 54
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\pages 1273--1279
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\vol 54
\issue 6
\pages 1013--1017
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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. V. V. Benyash-Krivets, I. O. Govorushko, “Mnogoobraziya predstavlenii podgrupp konechnogo indeksa grupp Baumslaga–Solitera”, Tr. In-ta matem., 23:2 (2015), 24–28  mathnet
    2. V. V. Benyash-Krivets, I. O. Govorushko, “Representation and character varieties of the Baumslag–Solitar groups”, Proc. Steklov Inst. Math., 292 (2016), 20–36  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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