Yangians and Mickelsson Algebras II

Details Yangians and Mickelsson Algebras II Yangians and Mickelsson Algebras II

2006-06-12

arxiv.org/abs/math/0606272v1

Moscow Mathematical Journal 6 (2006) 477-504

Mathematics

Representation Theory

26 pages

Scientific paper

We study a composition of two functors. The first one, from the category of modules over the Lie algebra $\gl_m$ to the category of modules over the degenerate affine Hecke algebra of $GL_N$, 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 $\Y(\gl_n)$ due to V. Drinfeld. We give a representation theoretic explanation of a link between intertwining operators on tensor products of $\Y(\gl_n)$-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 $\Y(\gl_n)$ discovered by G. Olshanski.

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