Irreducible monodromy matrices for the R-matrix of the XXZ-model and the lattice local quantum hamiltonians

Monodromy matrices possessing both a vacuum and a finite djmensional one-particle subspace for the R-matrix of the XXX and XXZ models are considered. A natural class of monodromy matrices, the irreducible ones, is described; for these matrices the statements suggested before as natural hypotheses are verified. For the quantum integrable models on a lattice with the irreducible local monodromy matrices the existence of local Hamiltonians is proved