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Izvestiya: Mathematics, 2009, Volume 73, Issue 6, Pages 1101–1109
DOI: https://doi.org/10.1070/IM2009v073n06ABEH002474 (Mi im4114) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On tilings related to discrete reflection groups

P. V. Bibikova, V. S. Zhgoonb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Scientific Research Institute for System Studies of RAS
English version PDF (249 kB) Citations (1) Russian version article
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DOI: https://doi.org/10.1070/IM2009v073n06ABEH002474
Abstract: We get simpler proofs of theorems of Waldspurger and Meinrenken on tilings formed by sets of the form (1−w)C∘, w∈W, where W is a linear or affine Weyl group and C∘ is the open kernel of a fundamental chamber C of W. We also generalize these results to cocompact hyperbolic reflection groups.
Keywords: discrete reflection group, fundamental chamber, dual cone, Brouwer fixed-point theorem.
Received: 18.05.2009
Bibliographic databases:
UDC: 512.817.72
MSC: 20F55, 05B45
Language: English
Original paper language: Russian
Citation: P. V. Bibikov, V. S. Zhgoon, “On tilings related to discrete reflection groups”, Izv. Math., 73:6 (2009), 1101–1109
Citation in format AMSBIB
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\by P.~V.~Bibikov, V.~S.~Zhgoon
\paper On tilings related to discrete reflection groups
\jour Izv. Math.
\yr 2009
\vol 73
\issue 6
\pages 1101--1109
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Linking options:
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  • https://doi.org/10.1070/IM2009v073n06ABEH002474
  • https://www.mathnet.ru/eng/im/v73/i6/p29
    • This publication is cited in the following 1 articles:
    1. P. V. Bibikov, “Relative angular measure of the dual cone of the fundamental cone of a finite reflection group”, Russian Math. Surveys, 65:1 (2010), 173–174  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:664
    Russian version PDF:245
    English version PDF:24
    References:66
    First page:24
     
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