On Lee association schemes over Z4 and their Terwilliger algebra

Let F = {0, 1, 2, 3} and define the set K = {K-0, K-1, K-2} of relations on F such that (x, y) epsilon K-i if and only if x - y equivalent to +/- i (mod 4). Let n be a positive integer. We consider the Lee association scheme L(n) over Z(4) which is the extension of length n of the initial scheme (F, K). Let T denote the Terwilliger algebra of L(n) with respect to the zero codeword of length n. We show that T is generated by a homomorphic image of the universal enveloping algebra of the Lie algebra s1(3)(C) and the center Z(T). Furthermore, we determine the irreducible modules for T using the Schur-Weyl duality. (C) 2016 Elsevier Inc. All rights reserved.