Multivariate Askey-Wilson functions and overlap coefficients
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916688246603776 |
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| author | Groenevelt, Wolter |
| author_facet | Groenevelt, Wolter |
| contents | We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic interpretation of the multivariate Askey-Wilson functions introduced by Geronimo and Iliev. We use the underlying coalgebra structure to derive $q$-difference equations satisfied by the multivariate Askey-Wilson functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariate Askey-Wilson functions and overlap coefficients Groenevelt, Wolter Quantum Algebra Classical Analysis and ODEs We study certain overlap coefficients appearing in representation theory of the quantum algebra $\U_q(\mathfrak{sl}_2(\C))$. The overlap coefficients can be identified as products of Askey-Wilson functions, leading to an algebraic interpretation of the multivariate Askey-Wilson functions introduced by Geronimo and Iliev. We use the underlying coalgebra structure to derive $q$-difference equations satisfied by the multivariate Askey-Wilson functions. |
| title | Multivariate Askey-Wilson functions and overlap coefficients |
| topic | Quantum Algebra Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2504.09735 |