Abstract
The classification problem of the admissible (with respect to the quaternionic structure of the Hilbert space) representations of the semi-simple compact Lie groups is considered. It is found that a symmetry group G must be of the form G=GF*Gc where the colour group Gc is isomorphic to the SU(3r) and r is odd. The natural selection rules generated by quaternionic structure are equivalent to the confinement of colour, i.e. total algebraic confinement of SU(3r)c degrees of freedom holds.
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