Everything you always wanted to know about SU(3) supset O(3)

Moshinsky M., Patera J., Sharp R.T., Winternitz P.

From a uniform viewpoint we discuss three old bases for representations of SU(3) reduced according to 0(3), the Bargmann-Moshinsky, Elliott and stretched bases, together with one new one, the antistretched basis. Expansions are obtained for the various bases in terms of each others and in terms of the Gel’fand basis of the SU(3) => SU(2) x U(l) scheme. Overlaps are given between states of the same or different bases. Orthogonal bases defined by diagonalization of a suitable Hermitian operators are discussed and related to the analytic bases.