Trions in a periodic potential
  The group-theoretical classification of trion states is presented. It is based on considerations of products of irreducible representations of the 2D translation group. For a given BvK period N degeneracy of obtained states is N^2. Trions consist of two identical particles so the symmetrization of states with respect to particles transposition is considered. Completely antisymmetric states can be constructed by introducing antisymmetric spin functions. Two symmetry adapted bases are considered. The third possibility is postponed for the further investigations. 
Wojciech Florek