Yangians and Mickelsson Algebras I

Details Yangians and Mickelsson Algebras I Yangians and Mickelsson Algebras I

2006-06-12

arxiv.org/abs/math/0606265v3

Transformation Groups 11 (2006) 625-658

Mathematics

Representation Theory

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

Scientific paper

10.1007/s00031-005-1125-2

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.

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