W-INFINITY ALGEBRAS IN THE QUANTUM HALL-EFFECT

We show that a large class of incompressible quantum Hall states corre spond to different representations of the W-infinity algebra by explic it construction of the second-quantized generators of the algebra in t erms of fermion and vortex operators. These are parametrized by a set of integers which are related to the filling fraction. The class of st ates we consider includes multilayer Hall states and the states propos ed by Jain to explain the hierarchical filling fractions. The correspo nding second-quantized order parameters are also given.