The $q$-Racah polynomials from scalar products of Bethe states
Pascal Baseilhac, Rodrigo A. Pimenta
TL;DR
This paper derives $q$-Racah polynomials as ratios of scalar products of Bethe states, linking algebraic Bethe ansatz and Leonard pairs to provide a new algebraic interpretation.
Contribution
It introduces a novel connection between $q$-Racah polynomials and scalar products of Bethe states using Leonard pairs and modified algebraic Bethe ansatz.
Findings
Expressed $q$-Racah polynomials via Bethe state scalar products
Linked Leonard pairs with Bethe ansatz methods
Provided algebraic interpretation of $q$-Racah polynomials
Abstract
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. This result is obtained by combining the theory of Leonard pairs and the modified algebraic Bethe ansatz.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry