Quaternionic symmetry groups and particle multiplets

We consider the quaternionic complete symmetry group of a massive physical system, obtained extending the connected Poincare group and the internal sy mmetry group by means of the CPT and the generalized parity operators. We c lassify the irreducible Q-representations of this group crossing the genera lized Wigner and Frobenius-Schur classifications, and obtain 14 different c ases. Some novelties arise in this context, such as the failure of the stat ement that only irreducible representations must be associated with particl e multiplets, and a suggestion on the possible forms of a parity-violating Hamiltonian. (C) 2000 American Institute of Physics. [S0022-2488(00)02707-9 ].