A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl(2)) via projective and Zuckerman functors

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dc.creatorBernstein, Joseph
dc.creatorFrenkel, Igor
dc.creatorKhovanov, Mikhail
dc.date2000-02-11
dc.date.accessioned2026-07-07T04:33:49Z
dc.date.available2026-07-07T04:33:49Z
dc.descriptionWe identify the Grothendieck group of certain direct sum of singular blocks of the highest weight category for sl(n) with the n-th tensor power of the fundamental (two-dimensional) sl(2)-module. The action of U(sl(2)) is given by projective functors and the commuting action of the Temperley-Lieb algebra by Zuckerman functors. Indecomposable projective functors correspond to Lusztig canonical basis in U(sl(2)). In the dual realization the n-th tensor power of the fundamental representation is identified with a direct sum of parabolic blocks of the highest weight category. Translation across the wall functors act as generators of the Temperley-Lieb algebra while Zuckerman functors act as generators of U(sl(2)).
dc.description31 pages, 11 figures
dc.identifierhttps://arxiv.org/abs/math/0002087
dc.identifierhttp://arxiv.org/abs/math/0002087
dc.identifierSelecta Mathematica, New ser. 5 (1999) 199--241
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58670
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B10
dc.titleA categorification of the Temperley-Lieb algebra and Schur quotients of U(sl(2)) via projective and Zuckerman functors
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