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27 April 2024

» arxiv » 1505.4386

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Annular Khovanov homology and knotted Schur-Weyl representations
J. Elisenda Grigsby ; Anthony M. Licata ; Stephan M. Wehrli ;
Date:	17 May 2015
Abstract:	Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n. One therefore obtains a "knotted" Schur-Weyl representation that agrees with classical sl_2 Schur-Weyl duality when K is the Seifert-framed unknot.
Source:	arXiv, 1505.4386
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