Yangians and Mickelsson algebras. II

We study the composition of two functors. The first functor, acting from the category of modules over the Lie algebra $\mathfrak{gl}_m$ to the category of modules over the degenerate affine Hecke algebra of $GL_N$, was introduced by Cherednik. The second functor is a skew version of the functor, due to Drinfeld, from the latter category to the category of modules over the Yangian $Y(\mathfrak{gl}_m)$. We give a representation-theoretic explanation of a link between intertwining operators on tensor products of $Y(\mathfrak{gl}_m)$-modules and the “extremal cocycle” introduced by Zhelobenko on the Weyl group of $\mathfrak{gl}_m$ We also establish a connection between the composition of two functors and Olshanski's “centralizer construction” of the Yangian $Y(\mathfrak{gl}_m)$.