Yangians and Mickelsson Algebras II

We study a composition of two functors. The first one, from the category of modules over the Lie algebra ${\text{gl}}_m$ to the category of modules over the degenerate affine Hecke algebra of $G{L}_N$, was introduced by I. Cherednik. The second functor is a skew version of the functor from the latter category to the category of modules over the Yangian $\text{Y}({\text{gl}}_n)$ due to V. Drinfeld. We give a representation theoretic explanation of a link between intertwining operators on tensor products of $\text{Y}({\text{gl}}_n)$-modules, and the extremal cocycle' on the Weyl group of $\gl_m$ introduced by D. Zhelobenko. We establish a connection between the composition of two functors, and the centralizer construction’ of the Yangian $\text{Y}({\text{gl}}_n)$ discovered by G. Olshanski.