Graduate Seminar

Location:  RI 208

Speaker: Adebola Evelyn Omotoye

MSc Student supervised by Allen Herman

Title:  Restricting Irreducible Representations of the Centralizer Algebra to the Terwilliger Algebra of an Association Scheme

 Abstract:

We will give the extent the algebraic structure of the Terwilliger algebra \((T=T_x(\mathcal{S}))\) of an association scheme with respect to a vertex \(x\) can be obtained from that of the centralizer algebra \(\tilde{T}=\tilde{T}_x(\mathcal{S})\) with respect to \(x\) of the scheme. Since \(T \subseteq \tilde{T}\) is known, it suffices to determine the decomposition of the restrictions of the irreducible \(\tilde{T}\)-modules to \(T\). In many cases, these remain irreducible, but as we will show, there are exceptions.

In this talk, we give an overview of the tools used to calculate the \(T\)-module decompositions of the irreducible  \(\tilde{T}\)-modules, and demonstrate the calculations for conjugacy class schemes of certain small groups.