  We give an explicit expression for the central elements of affine Hecke
algebras of type A in the Coxeter presentation, in terms of (parabolic) affine
Kazhdan-Lusztig polynomials. Our approach is based on a version of quantum
affine Schur-Weyl duality involving the Hall algebra of a cyclic quiver, on the
theory of canonical bases and on the higher-level q-deformed Fock spaces
recently introduced by Uglov.
