We have generalized recent results of Cappelli, Trugenberger and Zemba on the integer quantum Hall effect constructing explicitly a W 1+∞ for the fractional quantum Hall effect such that the negative modes annihilate the Laughlin wave functions. This generalization has a nice interpretation in Jain's composite fermion theory. Furthermore, for these models we have calculated the wave functions of the edge excitations viewing them as area preserving deformations of an incompressible quantum droplet, and have shown that the W 1+∞ is the underlying symmetry of the edge excitations in thefractional quantum Hall effect. Finally, we have applied this method to more general wave functions.
Product forms of characters of Virasoro minimal models are obtained which factorize into (2, odd) × (3, even) characters. These are related by generalized Rogers-Ramanujan identities to sum forms allowing for a quasiparticle interpretation. The corresponding dilogarithm identities are given and the factorization is used to analyse the related path space structure as well as the fusion of the maximally extended chiral algebra.
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