Factorization of the hypergeometric-type difference equation on the non-uniform lattices: dynamical algebra

Abstract

We argue that one can factorize the difference equation of hypergeometric type on the nonuniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra $s{u}_q(1,1)$, whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the $q$-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.

22 pages,

References in corpus (6)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• The q-harmonic oscillator and the Al-Salam and Carlitz polynomials
• The q-harmonic oscillator and an analog of the Charlier polynomials
• Meixner Oscillators
• Factorization method for difference equations of hypergeometric type on nonuniform lattices
• Discrete Darboux transformation for discrete polynomials of hypergeometric type

Cited by in corpus (3)

• On the Properties of Special Functions on the linear-type lattices
• The q-Racah-Krall-type polynomials
• The orthogonality of q-classical polynomials of the Hahn class: A geometrical approach