论文标题
从小组动作的角度重新审视的奇数图的Terwilliger代数
The Terwilliger algebra of the Odd graph revisited from the viewpoint of group action
论文作者
论文摘要
令$ o_ {m+1} $表示一组基数$ 2M+1 $上的奇数图，其中$ m $是一个正整数。用$ x $表示其顶点集和$ t：= t（x_0）$其terwilliger代数相对于任何固定的顶点$ x_0 \ in x $。在本文中，我们首先证明了$ t $与$ o_ {m+1} $的$ x_0 $稳定器的中央式代数相吻合，考虑了该自动形态组在$ x \ times x \ times x \ times x $ x $中。然后，我们通过使用$ v的所有均匀组件：= \ m athbb {c}^x $分解$ m \ geq 3 $，每个组件是由不可差的$ t $ - modules跨越$ v $的非零子空间的非零子空间。最后，我们为$ v $的每个均匀组件显示正交基础。
Let $O_{m+1}$ denote the Odd graph on a set of cardinality $2m+1$, where $m$ is a positive integer. Denote by $X$ its vertex set and by $T:=T(x_0)$ its Terwilliger algebra with respect to any fixed vertex $x_0\in X$. In this paper, we first prove that $T$ coincides with the centralizer algebra of the stabilizer of $x_0$ in the automorphism group of $O_{m+1}$ by considering the action of this automorphism group on $X\times X\times X$. Then we give the decomposition of $T$ for $m\geq 3$ by using all the homogeneous components of $V:=\mathbb{C}^X$, each of which is a nonzero subspace of $V$ spanned by the irreducible $T$-modules that are isomorphic. Finally, we display an orthogonal basis for every homogeneous component of $V$.
