English

$q$-deformed Griffiths polynomials of Racah type

Mathematical Physics 2024-10-28 v2 math.MP

Abstract

New bivariate Griffiths polynomials of qq-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 qq-deformation of the Griffiths polynomials of Racah type introduced previously by the authors and collaborators. The latter are recovered from the former by a q1q\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.

Keywords

Cite

@article{arxiv.2407.17016,
  title  = {$q$-deformed Griffiths polynomials of Racah type},
  author = {Nicolas Crampe and Luc Frappat and Julien Gaboriaud and Eric Ragoucy},
  journal= {arXiv preprint arXiv:2407.17016},
  year   = {2024}
}

Comments

36 pages. Title modified in comparison to v1 and clarification on the polynomiality added