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 Okl (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 O0l for various irreducible representations ( p,q) of SU (3).