Annular Khovanov homology and knotted Schur-Weyl representations

J. Elisenda Grigsby; Anthony M. Licata; Stephan M. Wehrli

doi:10.1112/s0010437x17007540

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arXiv · 1505.04386

Annular Khovanov homology and knotted Schur-Weyl representations

J. Elisenda Grigsby·Anthony M. Licata·Stephan M. Wehrli

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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.

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J. Elisenda Grigsby, Anthony M. Licata, Stephan M. Wehrli. 2015-05-17. Annular Khovanov homology and knotted Schur-Weyl representations. https://doi.org/10.1112/s0010437x17007540

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