论文标题
扭曲的格拉斯曼图的Terwilliger代数：薄盒
The Terwilliger algebra of the twisted Grassmann graph: the thin case
论文作者
论文摘要
有限连接的简单图$γ$相对于顶点$ x $的Terwilliger代数$ t（x）$是由邻接矩阵$ a $ a $ $γ$产生的复杂的半imple矩阵代数$（i = 0,1,2，\ dots）$，其中$ v_i $表示$ x $ $ i $的顶点的特征向量。 vanded grassmann图$ \ tilde {j} _q（2d+1，d）$ 2005年在其顶点套装上有两个自动形态组的轨道，并且众所周知，一个轨道具有$ t（x）$的属性。满足$ \ dim e_i^*（x）w \ leqslant 1 $ for All $ i $。在本文中，我们确定$ \ tilde {j} _q（2d+1，d）$的所有不可约$ t（x）$ - 用于此“薄”案例。
The Terwilliger algebra $T(x)$ of a finite connected simple graph $Γ$ with respect to a vertex $x$ is the complex semisimple matrix algebra generated by the adjacency matrix $A$ of $Γ$ and the diagonal matrices $E_i^*(x)=\operatorname{diag}(v_i)$ $(i=0,1,2,\dots)$, where $v_i$ denotes the characteristic vector of the set of vertices at distance $i$ from $x$. The twisted Grassmann graph $\tilde{J}_q(2D+1,D)$ discovered by Van Dam and Koolen in 2005 has two orbits of the automorphism group on its vertex set, and it is known that one of the orbits has the property that $T(x)$ is thin whenever $x$ is chosen from it, i.e., every irreducible $T(x)$-module $W$ satisfies $\dim E_i^*(x)W\leqslant 1$ for all $i$. In this paper, we determine all the irreducible $T(x)$-modules of $\tilde{J}_q(2D+1,D)$ for this "thin" case.
