Terwilliger Algebras of Wreath Powers of One-Class Association Schemes

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dc.creatorBhattacharyya, Gargi
dc.creatorSong, Sung Y.
dc.date2008-09-05
dc.date.accessioned2026-07-07T10:01:02Z
dc.date.available2026-07-07T10:01:02Z
dc.descriptionIn 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 $n=2$.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0809.1052
dc.identifierhttp://arxiv.org/abs/0809.1052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168509
dc.subjectCombinatorics
dc.subjectHistory and Overview
dc.subject05E30
dc.titleTerwilliger Algebras of Wreath Powers of One-Class Association Schemes
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