Griffiths polynomials of Racah type-Reference-Cited by-同舟云学术

Griffiths polynomials of Racah type

Published:2024-08-01 Issue:8 Volume:65 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Crampé Nicolas¹²^ORCID,Frappat Luc²^ORCID,Gaboriaud Julien³^ORCID,Ragoucy Eric²^ORCID,Vinet Luc⁴⁵^ORCID,Zaimi Meri⁴^ORCID

Affiliation:

1. Institut Denis-Poisson CNRS/UMR 7013 - Université de Tours - Université d’Orléans 1 , Parc de Grandmont, 37200 Tours, France

2. Laboratoire d’Annecy-le-Vieux de Physique Théorique LAPTh, Université Savoie Mont Blanc, CNRS 2 , F-74000 Annecy, France

3. Graduate School of Informatics, Kyoto University 3 , Sakyo-ku, Kyoto 606-8501, Japan

4. Centre de Recherches Mathématiques, Université de Montréal 4 , P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7, Canada

5. IVADO 5 , Montréal, Québec H2S 3H1, Canada

Abstract

Bivariate Griffiths polynomials of Racah type are constructed from univariate Racah polynomials. The bispectral properties of the former are deduced from simple properties of the latter. A duality relation and the orthogonality of these polynomials are provided. The domain of validity for the indices and variables of these polynomials is also determined. Particular limits on the parameters entering the polynomials allow to define several Griffiths polynomials of other types. One special limit connects them to the original Griffiths polynomials (of Krawtchouk type). Finally, a connection with the 9j symbols is made.

Publisher

AIP Publishing

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0209006/20111729/083507_1_5.0209006.pdf

Reference41 articles.

1. Bannai, E., Kurihara, H., Zhao, D., and Zhu, Y., “Multivariate P- and/or Q-polynomial association schemes,” arXiv:2305.00707 (2023).

2. SUq(3) corepresentations and bivariate q-Krawtchouk polynomials;J. Math. Phys.,2019

3. Bivariate P-polynomial association schemes;Algebraic Combinatorics,2024

4. Crampe, N., Frappat, L., Gaboriaud, J., Ragoucy, E., Vinet, L., and Zaimi, M., “λ-Griffiths polynomials: Bispectrality and biorthogonality,” arXiv:2311.03256 (2023).

5. The higher-rank Askey–Wilson algebra and its braid group automorphisms;SIGMA,2023