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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 4, Pages 90–92 (Mi faa131)  

This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

Reflection Subgroups of Reflection Groups

P. V. Tumarkin, A. A. Felikson

Independent University of Moscow

Abstract: Let $G$ be a discrete group generated by reflections in hyperbolic or Euclidean space, and let $H\subset G$ be a finite index reflection subgroup. Suppose that the fundamental chamber of $G$ is a finite volume polytope with $k$ facets. We prove that the fundamental chamber of $H$ has at least $k$ facets.

Keywords: reflection group, Coxeter polytope

DOI: https://doi.org/10.4213/faa131

Full text: PDF file (143 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2004, 38:4, 313–314

Bibliographic databases:

UDC: 512.817.72+514.174.5
Received: 31.03.2003

Citation: P. V. Tumarkin, A. A. Felikson, “Reflection Subgroups of Reflection Groups”, Funktsional. Anal. i Prilozhen., 38:4 (2004), 90–92; Funct. Anal. Appl., 38:4 (2004), 313–314

Citation in format AMSBIB
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\by P.~V.~Tumarkin, A.~A.~Felikson
\paper Reflection Subgroups of Reflection Groups
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 4
\pages 90--92
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\transl
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 4
\pages 313--314
\crossref{https://doi.org/10.1007/s10688-005-0011-y}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Felikson, A, “On hyperbolic Coxeter n-polytopes with n+2 facets”, Advances in Geometry, 7:2 (2007), 177  crossref  mathscinet  zmath  isi  scopus
    2. Felikson, A, “On hyperbolic Coxeter polytopes with mutually intersecting facets”, Journal of Combinatorial Theory Series A, 115:1 (2008), 121  crossref  mathscinet  zmath  isi  scopus
    3. Felikson, A, “REFLECTION SUBGROUPS OF Coxeter GROUPS”, Transactions of the American Mathematical Society, 362:2 (2010), 847  crossref  mathscinet  zmath  isi  scopus
    4. Felikson A., Tumarkin P., “Hyperbolic Subalgebras of Hyperbolic Kac-Moody Algebras”, Transform. Groups, 17:1 (2012), 87–122  crossref  mathscinet  zmath  isi  elib  scopus
    5. Felikson A., Tumarkin P., “Essential Hyperbolic Coxeter Polytopes”, Isr. J. Math., 199:1 (2014), 113–161  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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