Substitution Group and Mirror Reflection Symmetry in Special Unitary Groups

The substitutions leaving the character of the representation of the group SUn invariant are considered. The phases induced by these substitutions on the basis functions are established. The substitution giving the contragrediency transformation has been found. This transformation is interpreted as the reflection of the subspace of commuting operators and the corresponding coordinate systems with respect to the rest subspace. The application of the substitution group to the resolution of multiplicity problem in the case of SU 3 is demonstrated.