Degenerate affine Hecke algebras and centralizer construction for the symmetric groups

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dc.creatorMolev, A. I.
dc.creatorOlshanski, G. I.
dc.date2000-02-21
dc.date2000-02-22
dc.date.accessioned2026-07-07T04:33:58Z
dc.date.available2026-07-07T04:33:58Z
dc.descriptionIn our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We study the `stable' properties of the centralizers of S(n-m) in the group algebra C[S(n)] as n increases with m fixed. We construct a limit centralizer algebra A and describe its algebraic structure. The algebra A turns out to be closely related with the degenerate affine Hecke algebras. We also show that the so-called tame representations of the infinite symmetric group yield a class of natural A-modules.
dc.description45 pages
dc.identifierhttps://arxiv.org/abs/math/0002165
dc.identifierhttp://arxiv.org/abs/math/0002165
dc.identifierJ. Algebra 237 (2001), 302--341.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58730
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject20C05; 20C32
dc.titleDegenerate affine Hecke algebras and centralizer construction for the symmetric groups
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