The Terwilliger algebra of the incidence graph of the Hamming graph

摘要

Let be a distance-semiregular graph on Y, and let be the diameter of on Y. Let be the halved graph of on Y. Fix . Let T and be the Terwilliger algebras of and with respect to x, respectively. Assume, for an integer i with and for with , the numbers and depend only on i and do not depend on the choice of y, z. The first goal in this paper is to show the relations between T-modules of and -modules of . Assume is the incidence graph of the Hamming graph H(D, n) on the vertex set Y and the set of all maximal cliques. Then, satisfies above assumption and is isomorphic to H(D, n). The second goal is to determine the irreducible T-modules of . For each irreducible T-module W, we give a basis for W the action of the adjacency matrix on this basis and we calculate the multiplicity of W.