Relating Jack wavefunctions to WA_{k-1} theories

TL;DR

This paper proves that certain Jack polynomials used as wavefunctions in non-Abelian fractional quantum Hall systems are related to correlation functions in WA_{k-1} algebra models, establishing a deep mathematical connection.

Contribution

It provides a proof confirming the conjectured relation between Jack wavefunctions and WA_{k-1} minimal model correlation functions.

Findings

Confirmed the conjecture linking Jack polynomials to WA_{k-1} theories

Analyzed degenerate representations of WA_{k-1} models

Established a mathematical foundation for non-Abelian quantum Hall wavefunctions

Abstract

The (k,r)-admissible Jack polynomials, recently proposed as many-body wavefunctions for non-Abelian fractional quantum Hall systems, have been conjectured to be related to some correlation functions of the minimal model WA_{k-1}(k+1,k+r) of the WA_{k-1} algebra. By studying the degenerate representations of the WA_{k-1}(k+1,k+r) theory, we provide a proof for this conjecture.