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

Series of the solutions to Yang-Baxter equations: Hecke type matrices and descendant R-, L-operators