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Yangians and Mickelsson Algebras I

Khoroshkin, S. and Nazarov, M. (2006) Yangians and Mickelsson Algebras I. Transformation Groups, 11 (4). pp. 625-658. ISSN 1083-4362

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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.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 11 Feb 2009 14:40
Last Modified: 11 Feb 2009 14:40
Published Version: http://dx.doi.org/1007/s00031-005-1125-2
Status: Published
Publisher: Springer Verlag (Germany)
Identification Number: 10.1007/s00031-005-1125-2
URI: http://eprints.whiterose.ac.uk/id/eprint/7756

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