Abstract
The reduced system of Bethe equations is found for the threeâboson interaction. The invariants and surfaces in the space of Bethe parameters connected with this system are constructed. It is shown that on these surfaces the eigenvectors can be presented in a power form. The connection between Bethe ansatz and polynomial extensions of Lie algebras is briefly discussed. The computational procedures corresponding to the original Bethe equations and the method of polynomial algebras are compared.
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