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Algebra and Discrete Mathematics, 2017, том 23, выпуск 1, страницы 138–179
(Mi adm598)
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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
RESEARCH ARTICLE
Equivalence of Carter diagrams
Rafael Stekolshchik EFI Optitex Ltd
Аннотация:
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.
Ключевые слова:
Dynkin diagrams, Carter diagrams, Weyl group, cycles.
Поступила в редакцию: 22.12.2016
Образец цитирования:
Rafael Stekolshchik, “Equivalence of Carter diagrams”, Algebra Discrete Math., 23:1 (2017), 138–179
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm598 https://www.mathnet.ru/rus/adm/v23/i1/p138
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