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Griffiths polynomials of Racah type

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arxiv 2403.12148 v2 pith:YIX4DOLT submitted 2024-03-18 math-ph math.MP

Nicolas Crampe , Luc Frappat , Julien Gaboriaud , Eric Ragoucy , Luc Vinet , Meri Zaimi This is my paper · ORCID
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keywords polynomialsgriffithsracahtypepropertiesallowbispectralbivariate
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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.

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  1. The quantum loop algebra of $sl_2$ and $q$-Racah type bivariate functions

    math.QA 2026-07 conditional novelty 6.0 of 10

    Bivariate q-Racah-type functions are realized as overlaps of six distinguished eigenbases in tensor-product evaluation representations of L U_q sl2, one family linked to tridiagonal pairs and another conjecturally to ...

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