Webs and quantum skew Howe duality

Abstract

We give a diagrammatic presentation in terms of generators mod relations of the representation category of $U_q({\mathfrak{sl}}_n)$. More precisely, we produce all the relations among ${\mathrm{SL}}_{\mathrm{n}}$-webs, thus describing the full subcategory tensor-generated by fundamental representations ${\bigwedge }^k{\mathbb{C}}^n$ (this subcategory can be idempotent completed to recover the entire representation category). Our result answers a question posed by Kuperberg [arXiv:q-alg/9712003] and affirms conjectures of Kim [arXiv:math.QA/0310143] and Morrison [arXiv:0704.1503]. Our main tool is an application of quantum skew Howe duality.

32 pages, added a missing relation which had been implicitly used; this version has the same content as the published version

References in corpus (2)

• The sl_3 web algebra
• The Moduli Problem of Lobb and Zentner and the Coloured sl(N) Graph Invariant

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