这是群论和图论方向的线上系列报告，我们希望能够促进国内外青年学者（博士生为主）在群论和图论研究上的交流。报告主题分布在（但不限于）以下研究方向：
This is a platform for young group theorists and graph theorists (mostly PhD students) to talk about their research and related topics online. The topic can be anything related to group theory and graph theory, including but not limited to the following.
一般地，系列报告定期于北京时间每周三下午16:00-17:00进行。
Our usual time is Wednesday 16:00-17:00 (GMT+8).
Title: The Terwilliger algebras of the group association schemes of non-abelian
finite groups admitting an abelian subgroup of index 2
Speaker: 杨靖 Jing Yang (Central South University)
Time: 16:00-17:00 (GMT+8), Wednesday November 20th
Location: 腾讯会议: 95981353900 (passcode: 2024)
Abstract:
For any finite group \(G\), the Terwilliger algebra \(\mathcal{T}(G)\) of the group association scheme
satisfies the following inclusions: \(\mathcal{T}_0(G)\subseteq \mathcal{T}(G)\subseteq\widetilde{\mathcal{T}}(G)\),
where \(\mathcal{T}_0(G)\) is a specific vector space and \(\widetilde{\mathcal{T}}(G)\) is the centralizer algebra
of the permutation representation of \(G\) induced by the action of conjugation. The group \(G\) is said to be triply
transitive if \(\mathcal{T}_0(G)=\widetilde{\mathcal{T}}(G)\).In this paper, we determine the dimension of the
Terwilliger algebras of non-abelian finite groups admitting an abelian subgroup of index 2 by showing that they are
triply transitive. Moreover, we give a complete characterization of the Wedderburn components of the Terwilliger
algebras of these groups.
The seminar is currently based at the Southern University of Science and Technology (SUSTech, 南方科技大学).