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...
Saved in:
| Main Author: | |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849696047900655616 |
|---|---|
| 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]. |
| format | Article |
| id | doaj-art-cd1b15396dd447fd8ca997eaff709810 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |