Multipartite generalisation of the Schmidt decomposition
  We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class. 
H. A. Carteret, A. Higuchi and A. Sudbery