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# Talk: Factorization of the hypergeometric-type difference equation on the uniform lattice

Factorization of the hypergeometric-type difference equation on the uniform lattice

Date: 2005..07..25
Event: Conference on Difference Equations, Special Functions and Applications
Venue: Munich University of Technology, Germany

## Abstract

We argue that one can factorize the difference equation of hypergeometric type on non-uniform lattices in the 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 $$su_q(1,1)$$, 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.