  A collective vector-boson model with broken SU(3) symmetry, in which the
ground state band and the lowest $\gamma$ band belong to the same irreducible
representation but are non-degenerate, is applied to several deformed even-even
nuclei. The model description of ground and $\gamma$ bands together with the
corresponding B(E2) transition probabilities is investigated within a broad
range of SU(3) irreducible representations $(\lambda,\mu)$. The calculations
show that the $(\lambda,\mu)$ characteristics of rotational nuclei depend to a
great extent on the magnitude of the SU(3) splitting between the ground and
$\gamma$ bands. It is found that for weakly split spectra, the ground--$\gamma$
band coupling scheme is realized relevantly within narrow regions of
``favored'' $(\lambda,\mu)$ multiplets, while in the cases of strong splitting
a description in which the ground band is situated alone in an irreducible
representation is favored. The obtained results are analyzed in terms of the
bandmixing interactions. The possibility for a transition between the different
collective SU(3) schemes is discussed.
