Nonscalar extension of shift operator techniques for SU (3) in an O(3) basis. I. Theory

A set of relations is set up which connect quadratic products of the shift operators O k l (k = 0,1,2), which are nonscalar with respect to the O(3) subgroup of SU (3). The usefulness of these relations is illustrated by the calculation of the eigenvalues of the scalar shift operator O 0 l for various irreducible representations ( p,q) of SU (3).