Webs and quantum skew Howe duality

Sabin Cautis; Joel Kamnitzer; Scott Morrison

doi:10.1007/s00208-013-0984-4

Webs and quantum skew Howe duality

Sabin Cautis, Joel Kamnitzer, Scott Morrison^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

102 Citations (Scopus)

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.

Original language	English
Pages (from-to)	351-390
Number of pages	40
Journal	Mathematische Annalen
Volume	360
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-013-0984-4
Publication status	Published - 7 Sept 2014

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Webs and quantum skew Howe duality

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