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Algebra and Discrete Mathematics, 2005, выпуск 2, страницы 58–79
(Mi adm303)
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RESEARCH ARTICLE
Extended $G$-vertex colored partition algebras as centralizer algebras of symmetric groups
M. Parvathi, A. Joseph Kennedy Ramanujan Institute for Advanced Study in
Mathematics, University of Madras, Chennai – 600 005, India
Аннотация:
The Partition algebras $P_k(x)$ have been defined in [M1] and [Jo]. We introduce a new class of algebras for every group $G$ called "Extended $G$-Vertex Colored Partition Algebras," denoted by $\widehat{P}_{k}(x,G)$, which contain partition algebras $P_k(x)$, as subalgebras. We generalized Jones result by showing that for a finite group $G$, the algebra $\widehat{P}_{k}(n,G)$ is the centralizer algebra of an action of the symmetric group $S_n$ on tensor space $W^{\otimes k}$, where $W=\mathbb{C}^{n|G|}$. Further we show that these algebras $\widehat{P}_{k}(x,G)$ contain as subalgebras the "$G$-Vertex Colored Partition Algebras ${P_{k}(x,G)}$," introduced in [PK1].
Ключевые слова:
Partition algebra, centralizer algebra, direct product, wreath product, symmetric group.
Поступила в редакцию: 27.10.2003 Исправленный вариант: 16.07.2004
Образец цитирования:
M. Parvathi, A. Joseph Kennedy, “Extended $G$-vertex colored partition algebras as centralizer algebras of symmetric groups”, Algebra Discrete Math., 2005, no. 2, 58–79
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm303 https://www.mathnet.ru/rus/adm/y2005/i2/p58
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