The Terwilliger Algebra of a Hamming Digraph
数学专题报告
报告题目(Title)：The Terwilliger Algebra of a Hamming Digraph
报告人(Speaker)：Prof. Hiroshi Suzuki (International Chiristian University)
地点(Place)：教八 111
时间(Time)：2024 年 3 月 20 日（周三） 15:30--16:30
邀请人(Inviter)：吕本建、王恺顺
报告摘要
There is a long history of studying the Terwilliger algebra of distance-regular graphs. However, little is known about the Terwilliger algebras of a digraph or a nonsymmetric association scheme. We determine the irreducible modules of the Terwilliger algebra of a Hamming digraph $H^*(d,3)$, an infinite series of weakly distance regular digraphs whose symmetrization is distance regular. As is well known, the representation of the Terwilliger algebra of a binary Hamming graph $H(d,2)$ is closely related to that of the Lie algebra $\mathit{sl}_2(\mathbb{C})$. We show that in the case of $H^*(d,3)$, it is related to that of the Lie algebra $\mathit{sl}_3(\bC)$. We also identify the Terwilliger algebra of $H^*(d,3)$ as the $d$ symmetric tensor algebra of $\text{Mat}_3(\mathbb{C}$.
