Quantum symmetries of q-difference equations

Abstract

A general method is presented to determine the symmetry operators of linear q‐difference equations. It is applied to q‐difference analogs of the Helmoltz, heat, and wave equations in diverse dimensions. The symmetries are found to generate q‐deformations of classical Lie algebras. The method of separation of variables is used to obtain solutions which are seen to involve many basic special functions. This allows the derivation of various identities and formulas for these q‐functions.