  The W-infinity minimal models are conformal field theories which can describe
the edge excitations of the hierarchical plateaus in the quantum Hall effect.
In this paper, these models are described in very explicit terms by using a
bosonic Fock space with constraints, or, equivalently, with a non-trivial
Hamiltonian. The Fock space is that of the multi-component Abelian conformal
theories, which provide another possible description of the hierarchical
plateaus; in this space, the minimal models are shown to correspond to the
sub-set of states which satisfy the constraints. This reduction of degrees of
freedom can also be implemented by adding a relevant interaction to the
Hamiltonian, leading to a renormalization-group flow between the two theories.
Next, a physical interpretation of the constraints is obtained by representing
the quantum incompressible Hall fluids as generalized Fermi seas. Finally, the
non-Abelian statistics of the quasi-particles in the W-infinity minimal models
is described by computing their correlation functions in the Coulomb Gas
approach.
