A new parafermionic algebra associated with the homogeneous space $A^{ (2)}_2/U(1)$ and its corresponding $Z$-algebra have been recently proposed. In this paper, we give a free boson representation of the $A^{ (2)}_2$ parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a $W$-algebra type primary field with spin two.
Categories: hep-th cond-mat nlin.SI