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

Álvarez-Nodarse, R.; Atakishiyev, N. M. and Costas-Santos, R. S.**Journal of Physics A. Mathematical and General**38, no. 1 (2005), 153 — 174

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## Abstract

We argue that one can factorize the difference equation of hypergeometric type on the non-uniform 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 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.

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## BibTeX

@article {MR2126099, AUTHOR = {\'{A}lvarez-Nodarse, R. and Atakishiyev, N. M. and Costas-Santos, R. S.}, TITLE = {Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra}, JOURNAL = {J. Phys. A}, FJOURNAL = {Journal of Physics A. Mathematical and General}, VOLUME = {38}, YEAR = {2005}, NUMBER = {1}, PAGES = {153--174}, ISSN = {0305-4470}, MRCLASS = {39A13 (33D15)}, ZBL = {1079.33017}, MRNUMBER = {2126099}, MRREVIEWER = {Lucia Di Vizio}, DOI = {10.1088/0305-4470/38/1/011}, URL = {https://doi.org/10.1088/0305-4470/38/1/011}, }