Webs and quantum skew Howe duality

2012/10/31 by Sabin Cautis, Joel Kamnitzer, Scott Morrison · 3 citations
Mathematics · #math.RT #math.QA

paper · pdf · doi:10.1007/s00208-013-0984-4

published as Mathematische Annalen, October 2014, Volume 360, Issue 1-2, pp. 351-390 · 32 pages, added a missing relation which had been implicitly used; this version has the same content as the published version

arxiv created 2014/01/29 · arxiv updated 2015/09/03

Abstract

We give a diagrammatic presentation in terms of generators mod relations of the representation category of U_q(\mathfraksl_n). More precisely, we produce all the relations among \rmSL_n-webs, thus describing the full subcategory tensor-generated by fundamental representations \bigwedge^k ℂⁿ (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.

Citations

• Spiders for rank 2 Lie algebras
• A Diagrammatic Category for the Representation Theory of U_q(sl_n)

Cited by

• Presentations of Categories of Modules using the Cautis-Kamnitzer-Morrison Principle
• The quantum spin Brauer category
• Affine and cyclotomic q-Schur categories via webs

Related

• A categorification of the skew Howe action on a representation category of U_q(\mathfrakgl(m|n))
• sl(N)-Web categories
• On webs in quantum type C
• Quantum Webs of Type Q
• Mixed quantum skew Howe duality and link invariants of type A