On the clssification of multi-isometries
  We consider the classification, up to unitary equivalence, of commuting n-tuples of isometries. We pay special attention to the case when the product of the isometries is a shift of finite multiplicity, and we provide a complete classification when this multiplicity equals n. When n=2, we identify a pivotal operator which captures many of the properties of a bi-isometry. 
H. Bercovici, R. G. Douglas and C. Foias