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The -Racah polynomials from scalar products of Bethe states II
Pascal Baseilhac, Rodrigo A. Pimenta
The theory of Leonard triples is applied to the derivation of normalized scalar products of on-shell and off-shell Bethe states generated from a Leonard pair. The scalar products t…
The -Racah polynomials from scalar products of Bethe states
Pascal Baseilhac, Rodrigo A. Pimenta
The -Racah polynomials are expressed in terms of certain ratios of scalar products of Bethe states associated with Bethe equations of either homogeneous or inhomogeneous type. T…
Scalar product for the XXZ spin chain with general integrable boundaries
Samuel Belliard, Rodrigo A. Pimenta, Nikita A. Slavnov
We calculate the scalar product of Bethe states of the XXZ spin- chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer m…
Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
Pascal Baseilhac, Rodrigo A. Pimenta
An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the ge…
Higher rank classical analogs of the Askey-Wilson algebra from the Onsager algebra
Pascal Baseilhac, Nicolas Crampe, Rodrigo A. Pimenta
The -Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the -Onsager algebra is given, its current algebra and commu…
The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
Rafael I. Nepomechie, Rodrigo A. Pimenta, Ana L. Retore
A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) in…