Distance-regular graphs and the -tetrahedron algebra

Abstract: Let denote a distance-regular graph with classical parameters and , . The condition on implies that is formally self-dual. For we use the adjacency matrix and dual adjacency matrix to obtain an action of the -tetrahedron algebra on the standard module of . We describe four algebra homomorphisms into from the quantum affine algebra ; using these we pull back the above -action to obtain four actions of on the standard module of . [Copyright &y& Elsevier]