Some eigenstates for a model associated with solutions of tetrahedron equation. III. Tetrahedral Zamolodchikov algebras and perturbed strings

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This paper continues the series begun with works solv-int/9701016 and solv-int/9702004. Here we show how to construct eigenstates for a model based on tetrahedron equation using the tetrahedral Zamolodchikov algebras. This yields, in particular, new eigenstates for the model on infinite lattice -- `perturbed', or `broken', strings.
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