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.
Partition function of the trigonometric SOS model with reflecting end
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abstract
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
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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.