Triality Type and its Generalization in Unitary Symmetry Theories

Within the context of an extension of the SU₃‐symmetry theory recently suggested by Gell‐Mann and further developed by the authors, certain aspects of the theory of the special unitary groups are examined. The plurality type of a given representation is introduced as the generalization of the triality concept to SU_n+1 and is shown to be associated with a multiplicative conservation law. Theorems for the reduction of representations of SU_n+1 with respect to SU_n$\otimes$ U₁⁽ⁿ⁾ are derived which are subsequently used to relate plurality type to the existence of fractional eigenvalues for the generator Y₁⁽ⁿ⁾ of U₁⁽ⁿ⁾.