A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products

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dc.creatorFrenkel, Igor
dc.creatorKhovanov, Mikhail
dc.creatorStroppel, Catharina
dc.date2005-11-18
dc.date.accessioned2026-07-07T08:07:23Z
dc.date.available2026-07-07T08:07:23Z
dc.descriptionThe purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie algebra gl(n). For the special case of simple modules we naturally deduce a categorification via modules over the cohomology ring of certain flag varieties. Further geometric categorifications and the relation to Steinberg varieties are discussed. We also give a categorical version of the quantised Schur-Weyl duality and an interpretation of the (dual) canonical bases and the (dual) standard bases in terms of projective, tilting, standard and simple Harish-Chandra bimodules.
dc.identifierhttps://arxiv.org/abs/math/0511467
dc.identifierhttp://arxiv.org/abs/math/0511467
dc.identifierSelecta Mathematica 2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130925
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject20G42, 17B10, 14M15, 16G10
dc.titleA categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products
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