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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)
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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 $(1-w)C^\circ$, $w\in W$, where $W$ is a linear or affine Weyl group and $C^\circ$ 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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 6, Pages 29–38
DOI: https://doi.org/10.4213/im4114
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. RAN. Ser. Mat., 73:6 (2009), 29–38; Izv. Math., 73:6 (2009), 1101–1109
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v73/i6/p29
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    English version PDF:18
    References:53
    First page:24
     
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