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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…
Freidel-Maillet type presentations of
Pascal Baseilhac
A unified framework for the Chevalley and equitable presentation of is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pai…
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 Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type
Pascal Baseilhac, Satoshi Tsujimoto, Luc Vinet +1
The Heun-Askey-Wilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A ce…