2008/09/05 by Gargi Bhattacharyya, Bhattacharyya, Gargi, Sung Y. Song +1
Mathematics · #05E30 #Combinatorics (math.CO) #FOS: Mathematics #History and Overview (math.HO) #math.CO #math.HO #msc:05E30
paper · pdf · doi:10.48550/arxiv.0809.1052
27 pages
arxiv created 2008/09/05 · arxiv updated 2009/12/01
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 Kn=H(1, n) for n≥ 2. We find that the d-class association scheme K_n1\wr K_n2 \wr ... \wr K_nd formed by taking the wreath product of K_ni has the triple-regularity property. We determine the dimension of the Terwilliger algebra for the association scheme K_n1\wr K_n2\wr ... \wr K_ nd. We give a description of the structure of the Terwilliger algebra for the wreath power (Kn)\wr d for n ≥ 2 by studying its irreducible modules. In particular, we show that the Terwilliger algebra of (Kn)\wr d is isomorphic to Md+1(ℂ)⊕ M1(ℂ)⊕ \frac12d(d+1) for n≥3, and Md+1(ℂ)⊕ M1(ℂ)⊕ \frac12d(d-1) for n=2.