Many-Particle Translational Symmetries of Two-Dimensional Electrons at Rational Landau-Level Filling

In contrast to previous treatments, a new analysis of two-dimensional many-electron systems subject to periodic boundary conditions in a magnetic field leads to a fully two-dimensional structure of the quantum numbers at rational Landau-level filling. The structure of the new symmetry analysis has an intrinsically many-particle character. Full agreement between numerical studies of quantized-Hall-effect systems in periodic and spherical geometries is achieved, and the problem of ground-state degeneracy is clarified.