The quantum Knizhnik–Zamolodchikov equation and non-symmetric Macdonald polynomials

Abstract

We construct special solutions of the quantum Knizhnik-Zamolodchikov equation on the tensor product of the vector representation of the quantum algebra of type AN−1. They are constructed from non-symmetric Macdonald polynomials through the action of the affine Hecke algebra. As a special case the matrix element of the vertex operators of level one is reproduced.