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$q$-deformed Griffiths polynomials of Racah type

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arxiv 2407.17016 v2 pith:GV6JRRUC submitted 2024-07-24 math-ph math.MP

Nicolas Crampe , Luc Frappat , Julien Gaboriaud , Eric Ragoucy This is my paper · ORCID
classification math-phmath.MP
keywords polynomialsgriffithsintroducedracahtypetheyauthorsbiorthogonal
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abstract

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.

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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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