Graduate Seminar

Location:  CL 305 and Live Stream

Speaker: Adebola Omotoye

MSc Student supervised by Allen Herman

Title:  The Inclusion of the Terwilliger Algebra in the Centralizer Algebra of an Association Scheme

 Zoom Link:  https://uregina-ca.zoom.us/j/92805435386?pwd=42pEMT2QL4b8W8bqIOr5Y39hln8bSI.1

Abstract:

Terwilliger \( (T)\)-algebras are finite-dimensional semi-simple algebras introduced by Paul Terwilliger in 1992 in the study of association schemes. The algebraic structure of the\( T\)-algebra can be determined from its irreducible representations, which correspond to the centrally primitive idempotents (CPIs) of the algebra, but these are not easy to obtain. However, the \( T\)-algebra is contained in a subalgebra of \( M_n(\mathbb{C}) \) that centralizes a certain subgroup of the permutation matrices in the automorphism group of the scheme. The algebraic structure of this centralizer algebra can be easily determined from the irreducible decomposition of the permutation character of this subgroup. This algebra is known to be equal to \(T\)-algebra in some schemes. 

In this talk, we consider the case where equality does not hold. We seek to understand the irreducible representations of the \( T\)-algebra by restricting the irreducible modules of the centralizer algebra to the \( T\)-algebra. In the best scenarios, these restrictions remain irreducible.