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- W3100433565 abstract "We give a diagrammatic presentation in terms of generators and relations of the representation category of $$U_q({mathfrak {sl}}_n) $$ . More precisely, we produce all the relations among $$mathrm{{SL}}_n$$ -webs, thus describing the full subcategory $$otimes $$ -generated by fundamental representations $${textstyle bigwedge ^{k}_{}} {mathbb C}^n$$ (this subcategory can be idempotent completed to recover the entire representation category). Our result answers a question posed by Kuperberg in Commun Math Phys 180(1):109–151, (1996) and affirms conjectures of Kim in Graphical calculus on representations of quantum lie algebras, Ph. D. thesis, University of California, Davis, (2003) and Morrison in A Diagrammatic Category for the Representation Theory of $$U_qleft( {mathfrak {sl}}_nright) $$ . PhD thesis, University of California, Berkeley, (2007). Our main tool is an application of quantum skew Howe duality. This is the published version of arXiv:1210.6437 ." @default.
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- W3100433565 date "2014-04-05" @default.
- W3100433565 modified "2023-10-18" @default.
- W3100433565 title "Webs and quantum skew Howe duality" @default.
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- W3100433565 doi "https://doi.org/10.1007/s00208-013-0984-4" @default.
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