Quiver Varieties and Branching

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dc.creatorNakajima, Hiraku
dc.date2008-09-15
dc.date2009-01-11
dc.date.accessioned2026-07-07T12:27:55Z
dc.date.available2026-07-07T12:27:55Z
dc.descriptionBraverman and Finkelberg recently proposed the geometric Satake correspondence for the affine Kac-Moody group $G_\aff$ [Braverman A., Finkelberg M., arXiv:0711.2083]. They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of $G_{\mathrm{cpt}}$-instantons on $\R^4/\Z_r$ correspond to weight spaces of representations of the Langlands dual group $G_\aff^\vee$ at level $r$. When $G = \SL(l)$, the Uhlenbeck compactification is the quiver variety of type $\algsl(r)_\aff$, and their conjecture follows from the author's earlier result and I. Frenkel's level-rank duality. They further introduce a convolution diagram which conjecturally gives the tensor product multiplicity [Braverman A., Finkelberg M., Private communication, 2008]. In this paper, we develop the theory for the branching in quiver varieties and check this conjecture for $G=\SL(l)$.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/0809.2605
dc.identifierhttp://arxiv.org/abs/0809.2605
dc.identifierSIGMA 5 (2009), 003, 37 pages
dc.identifierdoi:10.3842/SIGMA.2009.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215371
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectRepresentation Theory
dc.subject14D21, 17B65
dc.titleQuiver Varieties and Branching
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