Jucys–Murphy elements and a presentation for partition algebras
Jucys–Murphy elements and a presentation for partition algebras
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Jucys–Murphy 元素和分区代数演示
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Enyang
中科院分区：
文献类型：
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作者：
J. Enyang
给出了划分代数的一个新的表示。这一表述是在为Halverson和Ram定义的划分代数Jucys-Murphy元素建立归纳公式的过程中发现的（Eur. 26：869-921，2005）。利用Schur-Weyl对偶性证明了我们的递归公式与Halverson和Ram给出的Jucys-Murphy元的原始定义是等价的。本文给出了分划代数Jucys-Murphy元的新表示和归纳公式，并在另一篇文章中给出了分划代数Jucys-Murphy元的正规表示.
We give a new presentation for the partition algebras. This presentation was discovered in the course of establishing an inductive formula for the partition algebra Jucys–Murphy elements defined by Halverson and Ram (Eur. J. Comb. 26:869–921, 2005). Using Schur–Weyl duality we show that our recursive formula and the original definition of Jucys–Murphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra Jucys–Murphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.