QUANTUM HALL FLUIDS AS W-INFINITY MINIMAL MODELS

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}.