Connection preserving deformations and q-semi-classical orthogonal polynomials

Abstract

We present a framework for the study of q-difference equations satisfied by q-semi-classical orthogonal systems. As an example, we identify the q-difference equation satisfied by a deformed version of the little q-Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for q-PVI. We obtain a parametrization of the associated linear problem in terms of orthogonal polynomial variables and find the relation between this parametrization and that of Jimbo and Sakai. © 2011 IOP Publishing Ltd & London Mathematical Society.