The $q$-Racah polynomials from scalar products of Bethe states II
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916660234944512 |
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| author | Baseilhac, Pascal Pimenta, Rodrigo A. |
| author_facet | Baseilhac, Pascal Pimenta, Rodrigo A. |
| contents | 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 take the form of linear combinations of $q$-Racah polynomials with coefficients depending on the off-shell parameters. Upon specializations, explicit solutions for the corresponding Belliard-Slavnov linear systems are obtained. It implies the existence of a determinant formula in terms of inhomogeneous Bethe roots for the $q$-Racah polynomials. Also, a set of relations that determines solutions (Bethe roots) of the corresponding Bethe equations of inhomogeneous type in terms of solutions of Bethe equations of homogenous type is obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_10310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $q$-Racah polynomials from scalar products of Bethe states II Baseilhac, Pascal Pimenta, Rodrigo A. Mathematical Physics Quantum Algebra Representation Theory 33D45, 81R50, 81U15 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 take the form of linear combinations of $q$-Racah polynomials with coefficients depending on the off-shell parameters. Upon specializations, explicit solutions for the corresponding Belliard-Slavnov linear systems are obtained. It implies the existence of a determinant formula in terms of inhomogeneous Bethe roots for the $q$-Racah polynomials. Also, a set of relations that determines solutions (Bethe roots) of the corresponding Bethe equations of inhomogeneous type in terms of solutions of Bethe equations of homogenous type is obtained. |
| title | The $q$-Racah polynomials from scalar products of Bethe states II |
| topic | Mathematical Physics Quantum Algebra Representation Theory 33D45, 81R50, 81U15 |
| url | https://arxiv.org/abs/2501.10310 |