Two-dimensional electron gas in a periodic potential and external magneticfield: States of pairs and three-particle systems

The group-theoretical classification of states of identical particle pairs is presented. Then obtained states are coupled with those of an antiparticl e to construct states of a three-particle system. Investigations are perfor med using products of irreducible projective representations of the 2D tran slation group. For a given Born-von Karman period N degeneracy of pair stat es is N, whereas three-particle states are N-2-fold degenerated. It has to be underlined that the case of even N is more complicated since pail states are labelled by four inequivalent irreducible projective representations. The problem of symmetry properties with respect to particles transposition is briefly discussed.