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

We have constructed series of the spectral parameter dependent solutions to the Yang-Baxter equations defined on the tensor product of reducible representations with a symmetry of quantum (super)algebra. These series are produced as descendant solutions from the slq(2)-invariant Hecke type Rrr(u)-matrices. The analogues of the matrices of Hecke type with the symmetry of the quantum super-algebra ospq(1|2) are obtained precisely. For the homogeneous solutions Rr2−1r2−1 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 RrR(u), extended Lax operators of Hecke type, also are suggested.