Correlators based on sl(2) Yangian symmetry and its quantum deformation are studied. Symmetric integral operators can be defined with such correlators as kernels. Yang-Baxter operators can be represented in this way. Particular Yangian symmetric correlators are related to the kernels of QCD parton evolution. The solution of the eigenvalue problem of Yangian symmetric operators is described. (C) 2016 The Authors. Published by Elsevier B.V.