{
  "id": "0809.1052",
  "version": "v1",
  "published": "2008-09-05T15:27:45.000Z",
  "updated": "2008-09-05T15:27:45.000Z",
  "title": "Terwilliger Algebras of Wreath Powers of One-Class Association Schemes",
  "authors": [
    "Gargi Bhattacharyya",
    "Sung Y. Song"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO",
    "math.HO"
  ],
  "abstract": "In this paper, we study the subconstituent algebras, also called as Terwilliger algebras, of association schemes that are obtained as the wreath product of one-class association schemes $K_n=H(1, n)$ for $n\\ge 2$. We find that the $d$-class association scheme $K_{n_{1}}\\wr K_{n_{2}} \\wr ... \\wr K_{n_{d}}$ formed by taking the wreath product of $K_{n_{i}}$ has the triple-regularity property. We determine the dimension of the Terwilliger algebra for the association scheme $K_{n_{1}}\\wr K_{n_{2}}\\wr ... \\wr K_ {n_{d}}$. We give a description of the structure of the Terwilliger algebra for the wreath power $(K_n)^{\\wr d}$ for $n \\geq 2$ by studying its irreducible modules. In particular, we show that the Terwilliger algebra of $(K_n)^{\\wr d}$ is isomorphic to $M_{d+1}(\\mathbb{C})\\oplus M_1(\\mathbb{C})^{\\oplus \\frac12d(d+1)}$ for $n\\ge3$, and $M_{d+1}(\\mathbb{C})\\oplus M_1(\\mathbb{C})^{\\oplus \\frac12d(d-1)}$ for $n=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-05T15:27:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30"
    ],
    "keywords": [
      "terwilliger algebra",
      "one-class association schemes",
      "wreath power",
      "wreath product",
      "subconstituent algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1052B"
    }
  }
}