2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217376We 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.no figure, we gave a proof of the conjecture in the second version; we modified section 4.2 of the first version to correct an error in Proposition 4.4 and give more general resultQuantum AlgebraRepresentation Theory39A13; 33C52; 81R50text