The Subconstituent Algebra of an Association Scheme (Part II)
The Subconstituent Algebra of an Association Scheme (Part II)
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DOI：
10.1023/a:1022480715311
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发表时间：
1993
影响因子：
0.8
通讯作者：
Paul M. Terwilliger
中科院分区：
文献类型：
--
作者：
Paul M. Terwilliger
这是上一期文章的续篇。在本节中，我们确定了aP-和q -多项式关联方案的子成分代数的一个薄的、不可约的模的结构。这样的模块自然与伦纳德系统联系在一起。模块的同构类由Leonard系统决定，而Leonard系统又由四个参数决定：端点、对偶端点、直径和一个附加参数。如果模块具有足够大的维度，则parameterf取由有界整数参数索引的某一组值中的一个。
This is a continuation of an article from the previous issue. In this section, we determine the structure of a thin, irreducible module for the subconstituent algebra of aP- andQ- polynomial association scheme. Such a module is naturally associated with a Leonard system. The isomorphism class of the module is determined by this Leonard system, which in turn is determined by four parameters: the endpoint, the dual endpoint, the diameter, and an additional parameterf. If the module has sufficiently large dimension, the parameterftakes one of a certain set of values indexed by a bounded integer parametere.