The symmetry of three-electron states in a quantized magnetic field

The states of itinerant electrons on the finite square lattice in a quantized magnetic field are discussed. The single-electron states are classified by irreducible representations (IRs) of the magnetic translation group.The representation correspond to the Landau level, whereas its basis functions are analogs of the cyclotronic orbits. The filling factor of the Landau level is considered in the frame of multi-electron functions. Corresponding states are classified by the IR of MTG as well as by the irreducible representation of a symmetric group (permuting the electrons) and a unitary group (permuting electron states). The discussion is restricted to the case when the magnetic flux per unit cell of the two-dimensional square lattice is a rational number in terms of magnetic flux quanta. The additional parameter of the model is the Hubbard interaction between electrons.