Jack Polynomials, W-algebras and application to Fractional Quantum Hall Effect

We examine Jack symmetric functions and certain W-algebras as schemes for generating fractioanl quantum Hall wavefunctions. We add substantially to the evidence that the Jack functions correspond to certain W-algebras, by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. Except for the Read-Rezayi series all of these Jack symmetric functions turn out to be nonunitary theories. We discuss the (perhaps optimistic) possibility that these approaches may have relevance to various physical quantum Hall systems. Open questions in the field, as well as why this is of importance to those concerned with real experiments, will also be discussed.