Annular Khovanov homology and knotted Schur–Weyl representations

By J. E. Grigsby, Anthony M. Licata, S. Wehrli. Compositio Mathematica, 2015

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Let $\mathbb{L}\subset A\times I$ be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of $\mathfrak{sl}_{2}(\wedge )$ , the exterior current algebra of $\mathfrak{sl}_{2}$ . When $\mathbb{L}$ is an $m$ -framed $n$ -cable of a knot $K\subset S^{3}$ , its sutured annular Khovanov homology carries a commuting action of the symmetric group $\mathfrak{S}_{n}$ . One therefore obtains a ‘knotted’ Schur–Weyl representation that agrees with classical $\mathfrak{sl}_{2}$ Schur–Weyl duality when $K$ is the Seifert-framed unknot.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e841343eff6e13b4dc08604dfedd6a874e1628c9

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Citations in the corpus

Quantum link homology via trace functor I (2016, methodology): “f oriented tangles on the quantum annular homology of cablings of K: cups and caps act via introducing or removing two cables, whereas a crossing switches two of them. The action was ﬁrst observed in [GLW15] in the non-quantized setting. We compute this action and show that it factors through the Jo”