The Planar Rook Algebra and Pascal's Triangle
The Planar Rook Algebra and Pascal's Triangle
复制标题
平面鲁克代数和帕斯卡三角形
DOI：
10.4171/lem/55-1-3
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发表时间：
2008
影响因子：
1.7
通讯作者：
Kathryn E Herbig
中科院分区：
文献类型：
--
作者：
Daniel E. Flath;Tom Halverson;Kathryn E Herbig
。甚至二项式coe客户的乘法结构也源于平面白嘴龙代数的表示理论，正如我们在分解或乘积表示时发现的那样。平面车代数是“图代数”的一个例子，对于我们的目的来说，它是一个三维代数，它的基是由图的集合和由图集中组合描述的乘法给出的。当基图不需要交叉时，就得到平面代数。有一个不断发展的平面代数理论是由V.Jones提出的（参见[Jo]），它使用了比我们在这里给出的更新的平面性定义。本文的主要目的是建立平面车代数CP的组合表示理论
. Even themultiplicative structure of the binomial coecients arises from the representa-tion theory of the planar rook algebras, as we discover upon decomposition oftensor product representations.The planar rook algebra is an example of a \diagram algebra," which forour purposes is a nite-dimensional algebra with a basis given by a collectionof diagrams and multiplication described combinatorially by diagram concate-nation. When the basis diagrams can be drawn without edge crossings, we geta planar algebra. There is a growing theory of planar algebras initiated by V.Jones (see [Jo]) that uses a more re ned de nition of planarity than what wegive here.The main goal of this paper is to work out the combinatorial representationtheory of the planar rook algebra CP