STABLE HIERARCHICAL QUANTUM HALL FLUIDS AS W-1+INFINITY MINIMAL MODELS

In this paper, we pursue our analysis of the W-1+infinity symmetry of the low-energy edge excitations of incompressible quantum Hall fluids, These excitations are described by (1 + 1)-dimensional effective fiel d theories, which are built by representations of the W-1+infinity alg ebra. Generic W-1+infinity theories predict many more fluids than the few, stable ones found in experiments. Here we identify a particular c lass of W-1+infinity theories, the minimal models, which are made of d egenerate representations only - a familiar construction in conformal field theory. The W-1+infinity minimal models exist for specific value s of the fractional Hall conductivity, which nicely fit the experiment al data and match the results of the Jain hierarchy of quantum Hall fl uids. We thus obtain a new hierarchical construction, which is based u niquely on the concept of quantum incompressible fluid and is independ ent of Jain's approach and hypotheses. Furthermore, a surprising non-a belian structure is found in the W-1+infinity minimal models: they pos sess neutral quark-like excitations with SU(m) quantum numbers and non -abelian fractional statistics. The physical electron is made of anyon and quark excitations. We discuss some properties of these neutral ex citations which could be seen in experiments and numerical simulations .