Algebraic Bethe ansatz for the six vertex model with upper triangular $K$-matrices

We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right $K$-matrices have an upper triangular form. We show that the main difficulty entailed by those form of the $K$-matrices is the construction of the excited states. However, it is possible to treat this problem with aid of an auxiliary transfer matrix and by means of a generalized creation operator.

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