The Terwilliger algebra of a Hamming scheme

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