Structure of the microscopic theory of the hierarchical fractional quantum Hall effect

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Abstract
The quantum numbers of the quasiparticles in the hierarchical fractional quantum Hall (FQH) states are derived with the use of microscopic electron wave functions. We discuss the relation between the effective theories of the hierarchical FQH effect and microscopic electronic wave functions first suggested by Haldane and Halperin. The rich internal structures (the topological orders) in the FQH states, which were first revealed in effective theory, are further confirmed by the microscopic theory.