The point groups of interest in this paper can be introduced in two ways. The first one consists in defining an abstract point group by giving its table of multiplications, and then classifying the states and operators in the fermion Fock space according to the relevant irreducible representations (irreps). The second one, which we follow below, is more intuitive, and consist in defining the symmetry operators in the Fock space first, and then identifying their multiplication tables and the corresponding group structures.
for even systems
for odd systems
and D
operators