  We have constructed series of the spectral parameter dependent solutions to
the Yang-Baxter equations defined on the tensor product of reducible
representations with symmetry of quantum algebra. These series are produced as
descendant solutions from the $sl_{q}(2)$-invariant Hecke type
$R^{r\;r}(u)$-matrices. The analogues of the matrices of Hecke type with the
symmetry of the quantum super-algebra $osp_q(1|2)$ are obtained precisely. For
the homogeneous solutions $R^{r^2-1\;r^2-1}$ there are constructed Hamiltonian
operators of the corresponding one-dimensional quantum integrable models, which
describe rather intricate interactions between different kind of spin states.
Centralizer operators defined on the products of the composite states are
discussed. The inhomogeneous series of the operators $R^{r\mathcal{R}}(u)$,
extended Lax operators of Hecke type, also are suggested.
