The Terwilliger algebra of a Hamming scheme H(d,q)H(d,q)

We compute the Terwilliger algebra of a Hamming scheme H(d,q)H(d,q). This algebra can be described as symmetric dd-tensors on the TT-algebra of H(1,q)H(1,q) which are all isomorphic for q>2q>2. We give the decomposition into simple bilateral ideals using the representation theory of GL(2,C)GL(2,C).