You are here: Seminars > 2024 > November 20th
Central South University
Time: 16:00-17:00 (GMT+8), Wednesday November 20th, 2024
Location: Zoom
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.
Host: 陈俊彦 Junyan Chen