The group U(5) may be taken as the degeneracy (respectively, dynamical
) group of five (respectively, four) equivalent oscillators or particl
es. Practical applications require the knowledge of a complete set of
independent tensors of arbitrary degree acting within a totally symmet
ric irreducible representation of U(5). These are built in the canonic
al chain and their components explicitly determined through a simple r
ealization of semimaximal tensors.