$q$-deformed Griffiths polynomials of Racah type
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916453275402240 |
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| author | Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric |
| author_facet | Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric |
| contents | New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a $q\to1$ limit. We show that these new polynomials are bispectral and biorthogonal. We also exhibit some symmetry relations that are essential in the proof of the bispectrality property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-deformed Griffiths polynomials of Racah type Crampe, Nicolas Frappat, Luc Gaboriaud, Julien Ragoucy, Eric Mathematical Physics 33D50, 33D80, 16G60 New bivariate Griffiths polynomials of $q$-Racah type are introduced and characterized. They generalize the polynomials orthogonal on the multinomial distribution introduced by R. Griffiths fifty years ago. They also correspond to a $q$-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a $q\to1$ limit. We show that these new polynomials are bispectral and biorthogonal. We also exhibit some symmetry relations that are essential in the proof of the bispectrality property. |
| title | $q$-deformed Griffiths polynomials of Racah type |
| topic | Mathematical Physics 33D50, 33D80, 16G60 |
| url | https://arxiv.org/abs/2407.17016 |