The tree method for multidimensional q-Hahn and q-Racah polynomials

TL;DR

This paper introduces a novel tree-based approach to construct and analyze multidimensional q-Hahn and q-Racah polynomials, providing new insights into their eigenfunctions and interrelations.

Contribution

The authors develop a tree method for multidimensional q-Hahn polynomials and define multidimensional q-Racah polynomials as connection coefficients, offering a new framework for these polynomials.

Findings

Multidimensional q-Hahn polynomials are eigenfunctions of a q-difference operator.

Multidimensional q-Racah polynomials can be expressed as products of one-dimensional q-Racah polynomials.

The tree method facilitates the factorization and connection of multidimensional polynomials.

Abstract

We develop a tree method for multidimensional q-Hahn polynomials. We define them as eigenfunctions of a multidimensional q-difference operator and we use the factorization of this operator as a key tool. Then we define multidimensional q-Racah polynomials as the connection coefficients between different bases of q-Hahn polynomials. We show that our multidimensional q-Racah polynomials may be expressed as product of ordinary one-dimensional q-Racah polynomial by means of a suitable sequence of transplantations of edges of the trees.