W INFINITE SYMMETRIES IN THE HIERARCHICAL QUASIPARTICLE STATES (LOWEST LANDAU LEVEL STATES) OF THE FRACTIONAL QUANTUM HALL SYSTEMS

Abstract

We investigate the W infinite symmetries in the theory of general fractional quantum Hall effects by using the lowest Landau level constraint approach. We find that there does exist a W infinite symmetric algebra for the fractional quantum Hall system with all the quasiparticles being restricted to the lowest Landau level. The corresponding generators can be used to generate the new degenerate wavefunctions of the lowest Landau level states by means of Laughlin and Halperin wavefunctions. Meanwhile, we find there still exists another W infinite symmetric algebra in the system, whose generators are used to generate the degenerate wavefunctions of the lowest Landau level for the anti-quasiparticles. We conclude that the FQH system can effectively be described by quasiparticle features or anti-quasiparticle features. We also show that the local part of the W infinite symmetric algebras is the magnetic translation operator of the general fractional quantum Hall system. We finally construct the operators of the single mode wave density excitations in the system and discuss their operator product relations.