Application of commutation relations to determine the eigenvalues of operators

A method is proposed for constructing operators that change the eigenvalues of the generators of a given representation of a Lie algebra, i.e., if these operators are applied to the eigenfunctions of a chosen generator $F_i$ they lead to different eigenfunctions of the same generator. Equations are obtained for determining the changes of the eigenvalues of the generators. The results obtained are applied to operators in the second-quantization representation.