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

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In this thesis, we study the T-algebras of symmetric association schemes that are obtained as the wreath product of H(1, m) for m ≥ 2. We find that the D-class association scheme K n 1 K n • • • K n D formed by taking the wreath product of one-class association schemes K n i = H(1, n i) has the triple-regularity property. We determine the dimension of the Talgebra for the association scheme K n 1 K n 2 • • • K n D. We also show that the wreath power (K m) D = K m K m • • • K m , D copies of K m , is formally self-dual. We give a complete description of the irreducible T-modules and the structure of T-algebra for (K m) D for m ≥ 2 by essentially studying the irreducible modules of 2 copies of K m and then extending it to the general case for D copies of K m. Through these calculations we obtain that the T-algebra for (K m) D is M D+1 (C) ⊕ C ⊕ 1 2 D(D+1) for m ≥ 3, and M D+1 (C) ⊕ C ⊕ 1 2 D(D−1) for m = 2.