A factorization method for q-Racah polynomials

TL;DR

This paper introduces a novel factorization technique for q-Racah polynomials, inspired by methods used for q-Hahn polynomials, utilizing q-difference operators instead of association schemes.

Contribution

It presents a new factorization approach for q-Racah polynomials that avoids association scheme theory, relying solely on manipulation of q-difference operators.

Findings

New factorization method for q-Racah polynomials

Avoids use of association schemes and Gel'fand pairs

Simplifies analysis using q-difference operators

Abstract

We develop a factorization method for q-Racah polynomials. It is inspired to the approach to q-Hahn polynomials based on the q-Johnson scheme but we do not use association scheme theory nor Gel'fand pairs, but only manipolation of q-difference operators.