The paper derives normalized scalar products of on-shell and off-shell Bethe states using Leonard triples, obtains explicit solutions of Belliard-Slavnov systems, and gives a determinant formula for q-Racah polynomials.
Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
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abstract
In this paper, we prove the off-shell equation satisfied by the transfer matrix associated with the XXZ spin-$\frac12$ chain on the segment with two generic integrable boundaries acting on the Bethe vector. The essential step is to prove that the expression of the action of a modified creation operator on the Bethe vector has an off-shell structure which results in an inhomogeneous term in the eigenvalues and Bethe equations of the corresponding transfer matrix.
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The $q$-Racah polynomials from scalar products of Bethe states II
The paper derives normalized scalar products of on-shell and off-shell Bethe states using Leonard triples, obtains explicit solutions of Belliard-Slavnov systems, and gives a determinant formula for q-Racah polynomials.