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Categorical geometric skew Howe duality

Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony

Description

We categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(Sln)by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(Sl2) which are related to representations of Uq(Sln) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometric...[Show more]

dc.contributor.authorCautis, Sabin
dc.contributor.authorKamnitzer, Joel
dc.contributor.authorLicata, Anthony
dc.date.accessioned2015-12-13T22:43:14Z
dc.date.available2015-12-13T22:43:14Z
dc.identifier.issn0020-9910
dc.identifier.urihttp://hdl.handle.net/1885/79110
dc.description.abstractWe categorify the R-matrix isomorphism between tensor products of minuscule representations of Uq(Sln)by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of Uq(Sl2) which are related to representations of Uq(Sln) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometric categorification of Reshitikhin-Turaev tangle invariants developed by the first two authors.
dc.publisherSpringer
dc.sourceInventiones Mathematicae
dc.titleCategorical geometric skew Howe duality
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume180
dc.date.issued2010
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.ariespublicationf5625xPUB7627
local.type.statusPublished Version
local.contributor.affiliationCautis, Sabin, Columbia University
local.contributor.affiliationKamnitzer, Joel, University of Toronto
local.contributor.affiliationLicata, Anthony, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage111
local.bibliographicCitation.lastpage159
local.identifier.doi10.1007/s00222-009-0227-1
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-11T10:11:20Z
local.identifier.scopusID2-s2.0-76549117905
CollectionsANU Research Publications

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