Smallness problem for quantum affine algebras and quiver varieties

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dc.creatorHernandez, David
dc.date2006-07-21
dc.date2008-02-10
dc.date.accessioned2026-07-07T10:02:37Z
dc.date.available2026-07-07T10:02:37Z
dc.descriptionThe geometric small property (Borho-MacPherson) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima (math.QA/0105173) for certain resolutions of quiver varieties (analogs of the Springer resolution) : for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination theorem for monomials of Frenkel-Reshetikhin q-characters that we establish for non necessarily simply-laced quantum affine algebras. We also refine results of (math.QA/0501202) and extend the main result to general simply-laced quantum affinizations, in particular to quantum toroidal algebras (double affine quantum algebras).
dc.description33 pages; accepted for publication in Annales Scientifiques de l'Ecole Normale Superieure
dc.identifierhttps://arxiv.org/abs/math/0607526
dc.identifierhttp://arxiv.org/abs/math/0607526
dc.identifierAnnales Scientifiques de l'Ecole Normale Superieure (4) 41 (2008), No. 2, 271-306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169033
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B37
dc.titleSmallness problem for quantum affine algebras and quiver varieties
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