On Lee association schemes over and their Terwilliger algebra

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• 作者：John Vincent S. Morales ^{moralesjohnvince@ims.is.tohoku.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05E30 ; 05C50 ; 15A04 ; 20C30 ; 33C45
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 December 2016
• 年：2016
• 卷：510
• 期：Complete
• 页码：311-328
• 全文大小：430 K

文摘

Let F={0,1,2,3}$F=\{0,1,2,3\}$ and define the set K={K₀,K₁,K₂}$K=\{K_0,K_1,K_2\}$ of relations on F   such that (x,y)∈K_i$(x,y)\in K_i$ if and only if $x-y\equiv \pm i(\text{mod}4)$. Let n   be a positive integer. We consider the Lee association scheme c25aeb6ae7b6ba16da00950c" title="Click to view the MathML source">L(n)$L(n)$ over Z₄${\mathbb{Z}}_4$ which is the extension of length n   of the initial scheme (F,K)$(F,K)$. Let T$\mathcal{T}$ denote the Terwilliger algebra of c25aeb6ae7b6ba16da00950c" title="Click to view the MathML source">L(n)$L(n)$ with respect to the zero codeword of length n  . We show that T$\mathcal{T}$ is generated by a homomorphic image of the universal enveloping algebra of the Lie algebra sl₃(C)${\mathfrak{sl}}_3(\mathbb{C})$ and the center Z(T)$Z(\mathcal{T})$. Furthermore, we determine the irreducible modules for T$\mathcal{T}$ using the Schur–Weyl duality.