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We consider open XXX spins chain with two general boundary matrices submittedto one constraint, which is equivalent to the possibility to put the twomatrices in a triangular form. We construct Bethe vectors from a generalizedalgebraic Bethe ansatz. As usual, the method also provides Bethe equations andtransfer matrix eigenvalues.

Algebraic Bethe ansatz for open XXX model with triangular boundary matrices