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The braid group surjects onto G2 tensor space

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Morrison, Scott

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Let V be the 7-dimensional irreducible representation of the quantum group Uq (g2). For each n, there is a map from the braid group Bn to the endomorphism algebra of the n-th tensor power of V, given by R matrices. Extending linearly to the braid group algebra, we get a map. Lehrer and Zhang have proved that map is surjective, as a special case of a more general result. Using Kuperberg's spider for G2, we give an elementary diagrammatic proof of this result.

dc.contributor.authorMorrison, Scott
dc.date.accessioned2015-12-07T22:53:12Z
dc.identifier.issn0030-8730
dc.identifier.urihttp://hdl.handle.net/1885/27757
dc.description.abstractLet V be the 7-dimensional irreducible representation of the quantum group Uq (g2). For each n, there is a map from the braid group Bn to the endomorphism algebra of the n-th tensor power of V, given by R matrices. Extending linearly to the braid group algebra, we get a map. Lehrer and Zhang have proved that map is surjective, as a special case of a more general result. Using Kuperberg's spider for G2, we give an elementary diagrammatic proof of this result.
dc.publisherUniversity of California
dc.rightsAuthor/s retain copyright
dc.sourcePacific Journal of Mathematics
dc.subjectKeywords: Braid group; G2; Representation theory; Spider; Tensor category
dc.titleThe braid group surjects onto G2 tensor space
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume249
dc.date.issued2011
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.ariespublicationu4743872xPUB53
local.type.statusPublished Version
local.contributor.affiliationMorrison, Scott, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage189
local.bibliographicCitation.lastpage198
local.identifier.doi10.2140/pjm.2011.249.189
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2016-02-24T11:22:58Z
local.identifier.scopusID2-s2.0-78751617413
local.identifier.thomsonID000286075000009
dcterms.accessRightsOpen Access
CollectionsANU Research Publications

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