Construction of a Lax Pair for the E6(1)q-Painlevé System

@article{Witte2012ConstructionOA,
  title={Construction of a Lax Pair for the E6(1)q-Painlev{\'e} System},
  author={Nicholas S. Witte and Christopher M. Ormerod},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2012},
  volume={8},
  pages={097}
}
  • N. Witte, C. Ormerod
  • Published 30 June 2012
  • Mathematics, Physics
  • Symmetry Integrability and Geometry-methods and Applications
We construct a Lax pair for the $E^{(1)}_6 $ $q$-Painleve system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices - the $q$-linear lattice - through a natural generalisation of the big $q$-Jacobi weight. As a by-product of our construction we derive the coupled first-order $q$-difference equations… 
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