Yangians and Mickelsson Algebras I

We study the composition of the functor from the category of modules over the Lie algebra $\mathfrak{gl}_m$ to the category of modules over the degenerate affine Hecke algebra of GLN introduced by I. Cherednik, with the functor from the latter category to the category of modules over the Yangian ${\rm Y}(\mathfrak{gl}_n)$ due to V. Drinfeld. We propose a representation theoretic explanation of a link between the intertwining operators on the tensor products of ${\rm Y}(\mathfrak{gl}_n)$ -modules, and the "extremal cocycle" on the Weyl group of $\mathfrak{gl}_m$ defined by D. Zhelobenko. We also establish a connection between the composition of the functors, and the "centralizer construction" of the Yangian ${\rm Y}(\mathfrak{gl}_n)$ discovered by G. Olshanski.