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

Published 27 Nov 2022 in math-ph, math.MP, and nlin.SI | (2211.14727v1)

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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