Let D ≥ 1 and q ≥ 3 be two integers. Let H(D) = H(D, q) denote the D-dimensional Hamming graph over a q-element set. Let T (D) denote the Terwilliger algebra of H(D). Let V (D) denote the standard T (D)-module. Let ω denote a complex scalar. We consider a unital associative algebra Kω defined by generators and relations. The generators are A and B. The relations are A2B − 2ABA + BA2 = B + ωA, B2A − 2BAB + AB2 = A + ωB. The algebra Kω is the case of the Askey–Wilson algebras corresponding to the Krawtchouk polynomials. The algebra Kω is isomorphic to U(sl2) when ω2 ≠ 1. We view V (D) as a K1− 2-module. We apply the Clebsch–Gordan rule for U(sl2) q to decompose V (D) into a direct sum of irreducible T (D)-modules.
|期刊||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|出版狀態||已出版 - 2023|