  Motivated by the close connection of tensor models to the SYK model, we use
representation theory to construct the complete set of gauge invariant
observables for bosonic and fermionic tensor models. Correlation functions of
the gauge invariant operators in the free theory are computed exactly. The
gauge invariant operators close a ring. The structure constants of the ring are
described explicitly. Finally, we construct a collective field theory
description of the bosonic tensor model.
