On the Affine Weyl group of type A˜n−1

We study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of weights. A˜n−1 is one of the crystallographic C...

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Main Author: Muhammad A. Albar
Format: Article
Language:English
Published: Wiley 1987-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171287000188
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author Muhammad A. Albar
author_facet Muhammad A. Albar
author_sort Muhammad A. Albar
collection DOAJ
description We study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of weights. A˜n−1 is one of the crystallographic Coxeter groups considered by Maxwell [3], [4].
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issn 0161-1712
1687-0425
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publishDate 1987-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-cd1b15396dd447fd8ca997eaff7098102025-08-20T03:19:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110114715410.1155/S0161171287000188On the Affine Weyl group of type A˜n−1Muhammad A. Albar0Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi ArabiaWe study in this paper the affine Weyl group of type A˜n−1, [1]. Coxeter [1] showed that this group is infinite. We see in Bourbaki [2] that A˜n−1 is a split extension of Sn, the symmetric group of degree n, by a group of translations and of lattice of weights. A˜n−1 is one of the crystallographic Coxeter groups considered by Maxwell [3], [4].http://dx.doi.org/10.1155/S0161171287000188presentationReidemeister-Schreier methodCoxeter group.
spellingShingle Muhammad A. Albar
On the Affine Weyl group of type A˜n−1
International Journal of Mathematics and Mathematical Sciences
presentation
Reidemeister-Schreier method
Coxeter group.
title On the Affine Weyl group of type A˜n−1
title_full On the Affine Weyl group of type A˜n−1
title_fullStr On the Affine Weyl group of type A˜n−1
title_full_unstemmed On the Affine Weyl group of type A˜n−1
title_short On the Affine Weyl group of type A˜n−1
title_sort on the affine weyl group of type a n 1
topic presentation
Reidemeister-Schreier method
Coxeter group.
url http://dx.doi.org/10.1155/S0161171287000188
work_keys_str_mv AT muhammadaalbar ontheaffineweylgroupoftypean1