Terwilliger algebras of wreath products of one-class association schemes

In this paper, we study the wreath product of one-class association schemes Kn =H(1, n) for n≥ 2. We show that the d-class association scheme Kn1 Kn2 · · · Knd formed by taking the wreath product of Kni (for ni ≥ 2) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of Kn1 Kn2 · · · Knd by studying its irreducible modules. In particular, we show that every non-primary module of this algebra is 1-dimensional.