  W_k structure underlying the tensverse realization of SU(2) at level k is
analyzed. Extension of the equivalence existing between covariant and
light-cone gauge realization of affine Kac-Moody algebra to W_k algebras is
given. Higher spin generators related to parafermions are extracted from the
operator product algebra of the generators and are showed to be written in
terms of only one free boson compactified on a circle.
