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Annular Khovanov homology and knotted Schur-Weyl representations

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arxiv 1505.04386 v1 pith:QA6K74L3 submitted 2015-05-17 math.GT math.QAmath.RT

J. Elisenda Grigsby , Anthony M. Licata , Stephan M. Wehrli This is my paper · ORCID
classification math.GTmath.QAmath.RT
keywords annularhomologykhovanovschur-weylactionalgebracarriesknotted
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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.

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  1. Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic

    math.GT 2024-12 conditional novelty 6.0 of 10

    A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.

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