English

Connection preserving deformations and $q$-semi-classical orthogonal polynomials

Exactly Solvable and Integrable Systems 2010-05-10 v2

Abstract

We present a framework for the study of qq-difference equations satisfied by qq-semi-classical orthogonal systems. As an example, we identify the qq-difference equation satisfied by a deformed version of the little qq-Jacobi polynomials as a gauge transformation of a special case of the associated linear problem for qq-PVI\mathrm{P}_{\mathrm{VI}}. We obtain a parameterization of the associated linear problem in terms of orthogonal polynomial variables and find the relation between this parameterization and that of Jimbo and Sakai.

Keywords

Cite

@article{arxiv.0906.0640,
  title  = {Connection preserving deformations and $q$-semi-classical orthogonal polynomials},
  author = {Christopher M. Ormerod and Nicholas S. Witte and Peter J. Forrester},
  journal= {arXiv preprint arXiv:0906.0640},
  year   = {2010}
}

Comments

32 Pages, extended the study of the recursion relations, more references

R2 v1 2026-06-21T13:09:05.424Z