Factorized $A_2$-Leonard pair
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914715725201408 |
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| author | Crampe, Nicolas Zaimi, Meri |
| author_facet | Crampe, Nicolas Zaimi, Meri |
| contents | The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized $A_2$-Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the ($q$-)Askey scheme. The most general examples are associated to an intricate product of univariate ($q$-)Hahn and dual ($q$-)Hahn polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08312 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Factorized $A_2$-Leonard pair Crampe, Nicolas Zaimi, Meri Rings and Algebras Mathematical Physics Classical Analysis and ODEs Representation Theory The notion of factorized $A_2$-Leonard pair is introduced. It is defined as a rank 2 Leonard pair, with actions in certain bases corresponding to the root system of the Weyl group $A_2$, and with some additional properties. The functions arising as entries of transition matrices are bivariate orthogonal polynomials (of Tratnik type) with bispectral properties. Examples of factorized $A_2$-Leonard pairs are constructed using classical Leonard pairs associated to families of orthogonal polynomials of the ($q$-)Askey scheme. The most general examples are associated to an intricate product of univariate ($q$-)Hahn and dual ($q$-)Hahn polynomials. |
| title | Factorized $A_2$-Leonard pair |
| topic | Rings and Algebras Mathematical Physics Classical Analysis and ODEs Representation Theory |
| url | https://arxiv.org/abs/2312.08312 |