QUANTUM HALL FLUIDS AS W-INFINITY MINIMAL MODELS

Abstract

We review our recent work on the algebraic characterization of quantum Hall fluids. Specifically, we explain how the incompressible quantum fluid ground states can be classified by effective edge field theories with the W-infinity dynamical symmetry of ``quantum area-preserving diffeomorphisms''. Using the representation theory of W-infinity, we show how all fluids with filling factors $\nu =m/(pm+1)$ and $\nu =m/(pm-1)$ with $m$ and $p$ positive integers, $p$ even, correspond exactly to the W-infinity {\it minimal models}.

28 pages,plain LaTeX,proceedings of the conference on ``Statistical Mechanics and Quantum Field Theory'',U.S.C., Los Angeles (U.S.A.),May 1994 and of the summer school on ``Particles, Fields and Strings'',Banff (Canada), August 1994.