  The structure of the $\Delta J = 1$ doublet bands in $^{128}Cs$ is
investigated within the framework of the Interacting Vector Boson Fermion Model
(IVBFM). A new, purely collective interpretation of these bands is given on the
basis of the used boson-fermion dynamical symmetry of the model. The energy
levels of the doublet bands as well as the absolute $B(E2)$ and $B(M1)$
transition probabilities between the states of both yrast and yrare bands are
described quite well. The observed odd-even staggering of both $B(M1)$ and
$B(E2)$ values is reproduced by the introduction of an appropriate interaction
term of quadrupole type, which produces such a staggering effect in the
transition strengths. The calculations show that the appearance of doublet
bands in certain odd-odd nuclei could be a consequence of the realization of a
larger dynamical symmetry based on the non-compact supersymmetry group
$OSp(2\Omega /12, R)$.
