Vacuum-like state analysis of the representations of the para-Fermi operators

Using the underlying Lie-algebraical structure of a given number n of para-Fermi operators (PFO), the author studies the set of all finite dimensional representations of these operators. The sub-space of all vacuum-like states, i.e. vectors from the representation space on which the para-Fermi annihilation operators vanish is determined and it is shown that this space carries an irreducible representation of the algebra SU(n). An explicit formula for the number of the linearly independent vacuum-like states which appear within an arbitrarily given irreducible representation of PFO is derived. (11 refs).