Categories of modules over an affine Kac-Moody algebra and the Kazhdan-Lusztig tensor product

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dc.creatorYakimov, Milen
dc.date2002-10-11
dc.date2004-10-04
dc.date.accessioned2026-07-07T04:51:52Z
dc.date.available2026-07-07T04:51:52Z
dc.descriptionTo each category C of modules of finite length over a complex simple Lie algebra g, closed under tensoring with finite dimensional modules, we associate and study a category Aff(C)_κof smooth modules (in the sense of Kazhdan and Lusztig [KL1]) of finite length over the corresponding affine Kac-Moody algebra in the case of central charge less than the critical level. Equivalent characterizations of these categories are obtained in the spirit of the works of Kazhdan-Lusztig [KL1] and Lian-Zuckerman [LZ1]. In the main part of this paper we establish a finiteness result for the Kazhdan-Lusztig tensor product which can be considered as an affine version of a theorem of Kostant [K]. It contains as special cases the finiteness results of Kazhdan, Lusztig [KL] and Finkelberg [F], and states that for any subalgebra f of g which is reductive in g the "affinization" of the category of finite length admissible (g, f) modules is stable under Kazhdan-Lusztig's tensoring with the "affinization" of the category of finite dimensional g modules (which is O_κin the notation of [KL1, KL2, KL3]).
dc.description19 pages, AMS-Latex, v2 contains several minor changes
dc.identifierhttps://arxiv.org/abs/math/0210180
dc.identifierhttp://arxiv.org/abs/math/0210180
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65261
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.titleCategories of modules over an affine Kac-Moody algebra and the Kazhdan-Lusztig tensor product
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