The Terwilliger Algebra of the Incidence Graphs of Johnson Geometry
The Terwilliger Algebra of the Incidence Graphs of Johnson Geometry
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DOI：
10.37236/3751
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发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Qian Kong;Benjian Lv;Kaishun Wang
中科院分区：
文献类型：
--
作者：
Qian Kong;Benjian Lv;Kaishun Wang
设J （n, m, m + 1）表示约翰逊几何的入射图。众所周知，Johnson图J （n, m）是J （n, m, m + 1）的二分图。设T和T '分别是J （n, m, m + 1）和J （n, m）的Terwilliger代数。本文主要讨论了不可约T模的结构，从而完全确定了T。进一步，我们发现了T的不可约模与T '之间的关系。结果，代数T '又被确定了。
Let J ( n , m , m + 1 ) denote the incidence graph of Johnson geometry. It is well known that the Johnson graph J ( n , m ) is a halved graph of J ( n , m , m + 1 ) . Let T and T ' be the Terwilliger algebra of J ( n , m , m + 1 ) and J ( n , m ) , respectively. In this paper, we focus on the structures of irreducible T -modules, and then completely determine T . Furthermore, we discover the relationship between irreducible modules of T and T ' . As a result, the algebra T ' is determined again.