Terwilliger algebras of wreath products of association schemes

The Terwilliger algebra of an association scheme of order n introduced in [13] is a subalgebra of the matrix algebra of all n×n matrices. Terwilliger algebras of wreath products of special association schemes are studied in several papers. In this paper we study the Terwilliger algebra of the wreath product T≀S of two arbitrary association schemes S and T. We will express the Terwilliger algebra of T≀S and its primitive central idempotents in terms of the Terwilliger algebras of S and T and their primitive central idempotents. The known results of Hanaki, Kim, etc. (cf. [7,10]) are special cases of our results.