Symmetry, Integrability and Geometry: Methods and Applications (Jan 2009)
The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials
Abstract
We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra gl_N. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We prove that our solutions contain those obtained as a scaling limit of matrix elements of the vertex operators of level one.