The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme
The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme
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DOI：
10.1016/j.disc.2004.12.001
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发表时间：
2005-03
期刊：
影响因子：
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通讯作者：
IV JohnS.Caughman;Mark S. MacLean;Paul M. Terwilliger
中科院分区：
文献类型：
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作者：
IV JohnS.Caughman;Mark S. MacLean;Paul M. Terwilliger
设Y表示D小于3的D类对称关联方案，并假设Y是近二部P-和q -多项式。设x表示Y的一个顶点，设T=T(x)表示对应的Terwilliger代数。证明了任何不可约t模W在Terwilliger意义上都是薄的和对偶薄的。我们为W生成两种碱基，并描述T在这两种碱基上的作用。我们证明了t模W的同构类是由W的对偶端点和直径两个参数决定的。我们找到了一个递推式，给出了标准模中不可约t模的多重性。我们计算了那些直径至少为D-3的不可约t模的多重性。
Let Y denote a D-class symmetric association scheme with D⩾3, and suppose Y is almost-bipartite P- and Q-polynomial. Let x denote a vertex of Y and let T=T(x) denote the corresponding Terwilliger algebra. We prove that any irreducible T-module W is both thin and dual thin in the sense of Terwilliger. We produce two bases for W and describe the action of T on these bases. We prove that the isomorphism class of W as a T-module is determined by two parameters, the dual endpoint and diameter of W. We find a recurrence which gives the multiplicities with which the irreducible T-modules occur in the standard module. We compute this multiplicity for those irreducible T-modules which have diameter at least D-3.