Abstract
Using the method of projection operators we have constructed the basis of the irreducible representation D ▪ of the exceptional Lie group G 2 corresponding to the reduction of this group to the subgroup SU 3. The basis is nonorthogonal but convenient for calculations. The matrices of the generators of the group G 2 in this basis have been found. The problem of additional quantum number ω required for the complete labelling of the basis vectors is considered. For this purpose we introduce the operator ω which is cubic with respect to the generators of the group G 2 and scalar with respect to the subgroup SU 3. The matrix of this operator has been calculated in the nonorthogonal basis. This matrix has a nondegenerate spectrum of eigenvalues ω which can be used as the missing quantum number.
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