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The $q$-Racah polynomials from scalar products of Bethe states

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arxiv 2211.14727 v1 pith:J2TL43ST submitted 2022-11-27 math-ph math.MPnlin.SI

Pascal Baseilhac , Rodrigo A. Pimenta This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords bethepolynomialsproductsracahscalarstatesalgebraicansatz
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abstract

The $q$-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. This result is obtained by combining the theory of Leonard pairs and the modified algebraic Bethe ansatz.

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  1. The $q$-Racah polynomials from scalar products of Bethe states II

    math-ph 2025-01 conditional novelty 6.0 of 10

    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.

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