Terwilliger algebras of wreath products of one-class association schemes

• DOI: 10.1007/s10801-009-0196-x
• Publication Date: 2009-07-15T13:22:09Z
• Authors: Gargi Bhattacharyya; Sung Y. Song; Rie Tanaka
• Keywords: 0101 mathematics; 01 natural sciences

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 $K_{n_{1}}\wr K_{n_{2}}\wr \cdots \wr K_{n_{d}}$ 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 $K_{n_{1}}\wr K_{n_{2}}\wr \cdots \wr K_{n_{d}}$ by studying its irreducible modules. In particular, we show that every non-primary module of this algebra is 1-dimensional.