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We propose a new way for describing the transition between two quantum Halleffect states with different filling factors within the framework of rationalconformal field theory. Using a particular class of non-unitary theories, weexplicitly recover Jain's picture of attaching flux quanta by the fusion rulesof primary fields. Filling higher Landau levels of composite fermions can bedescribed by taking tensor products of conformal theories. The usual projectionto the lowest Landau level corresponds then to a simple coset of these tensorproducts with several U(1)-theories divided out. These two operations -- thefusion map and the tensor map -- can explain the Jain series and all otherobserved fractions as exceptional cases. Within our scheme of transitions wenaturally find a field with the experimentally observed universal criticalexponent 7/3.

FUSION AND TENSORING OF CONFORMAL FIELD THEORY AND COMPOSITE FERMION PICTURE OF FRACTIONAL QUANTUM HALL EFFECT