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arXiv · 2407.17016

$q$-deformed Griffiths polynomials of Racah type

Nicolas Crampe·Luc Frappat·Julien Gaboriaud·Eric Ragoucy
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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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Nicolas Crampe, Luc Frappat, Julien Gaboriaud, Eric Ragoucy. 2024-07-24. $q$-deformed Griffiths polynomials of Racah type. https://arxiv.org/abs/2407.17016

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