Equivalence of Carter diagrams
We introduce the equivalence relation \(\rho\) on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing \(l\)-cycles with \(l > 4\) to an equivalent Carter diagram containing only \(4\)-cycles. Transforming one Carter diagram \(\Gamma_1\) to anot...
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| Дата: | 2017 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2017
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/370 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-3702017-04-10T07:40:45Z Equivalence of Carter diagrams Stekolshchik, Rafael Dynkin diagrams, Carter diagrams, Weyl group, cycles 20F55 We introduce the equivalence relation \(\rho\) on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing \(l\)-cycles with \(l > 4\) to an equivalent Carter diagram containing only \(4\)-cycles. Transforming one Carter diagram \(\Gamma_1\) to another Carter diagram \(\Gamma_2\) we can get a certain intermediate diagram \(\Gamma'\) which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation \(\rho\) is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams. Lugansk National Taras Shevchenko University 2017-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/370 Algebra and Discrete Mathematics; Vol 23, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/370/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/370/188 Copyright (c) 2017 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Dynkin diagrams Carter diagrams Weyl group cycles 20F55 |
| spellingShingle |
Dynkin diagrams Carter diagrams Weyl group cycles 20F55 Stekolshchik, Rafael Equivalence of Carter diagrams |
| topic_facet |
Dynkin diagrams Carter diagrams Weyl group cycles 20F55 |
| format |
Article |
| author |
Stekolshchik, Rafael |
| author_facet |
Stekolshchik, Rafael |
| author_sort |
Stekolshchik, Rafael |
| title |
Equivalence of Carter diagrams |
| title_short |
Equivalence of Carter diagrams |
| title_full |
Equivalence of Carter diagrams |
| title_fullStr |
Equivalence of Carter diagrams |
| title_full_unstemmed |
Equivalence of Carter diagrams |
| title_sort |
equivalence of carter diagrams |
| description |
We introduce the equivalence relation \(\rho\) on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing \(l\)-cycles with \(l > 4\) to an equivalent Carter diagram containing only \(4\)-cycles. Transforming one Carter diagram \(\Gamma_1\) to another Carter diagram \(\Gamma_2\) we can get a certain intermediate diagram \(\Gamma'\) which is not necessarily a Carter diagram. Such an intermediate diagram is called a connection diagram. The relation \(\rho\) is the equivalence relation on the set of Carter diagrams and connection diagrams. The properties of connection and Carter diagrams are studied in this paper. The paper contains an alternative proof of Carter's classification of admissible diagrams. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/370 |
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AT stekolshchikrafael equivalenceofcarterdiagrams |
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2024-04-12T06:25:43Z |
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2024-04-12T06:25:43Z |
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