English

Yangians and Mickelsson Algebras I

Representation Theory 2012-04-20 v3 Quantum Algebra

Abstract

We study the composition of the functor 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 introduced by I. Cherednik, with the functor from the latter category to the category of modules over the Yangian Y(gl_n) due to V. Drinfeld. We propose a representation theoretic explanation of a link between the intertwining operators on the tensor products of Y(gl_n)-modules, and the `extremal cocycle' on the Weyl group of gl_m defined by D. Zhelobenko. We also establish a connection between the composition of two functors, and the `centralizer construction' of the Yangian Y(gl_n) discovered by G. Olshanski.

Keywords

Cite

@article{arxiv.math/0606265,
  title  = {Yangians and Mickelsson Algebras I},
  author = {Sergey Khoroshkin and Maxim Nazarov},
  journal= {arXiv preprint arXiv:math/0606265},
  year   = {2012}
}

Comments

publication details added. arXiv admin note: substantial text overlap with arXiv:math/0606272

R2 v1 2026-07-22T17:37:16.758Z