Webs and quantum skew Howe duality

Abstract

We give a diagrammatic presentation in terms of generators and relations of the representation category of (formula presented) More precisely, we produce all the relations among (formula presented) -webs, thus describing the full subcategory (formula presented) -generated by fundamental representations (formula presented) (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 (formula presented). 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.