Annular Khovanov homology and knotted Schur-Weyl representations

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

doi:10.1112/S0010437X17007540

Annular Khovanov homology and knotted Schur-Weyl representations

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Let be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of , the exterior current algebra of . When is an -framed -cable of a knot , its sutured annular Khovanov homology carries a commuting action of the symmetric group . One therefore obtains a 'knotted' Schur-Weyl representation that agrees with classical Schur-Weyl duality when is the Seifert-framed unknot.

Original language	English (US)
Pages (from-to)	459-502
Number of pages	44
Journal	Compositio Mathematica
Volume	154
Issue number	3
DOIs	https://doi.org/10.1112/S0010437X17007540
State	Published - Mar 1 2018

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X17007540

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abstract = "Let be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of , the exterior current algebra of . When is an -framed -cable of a knot , its sutured annular Khovanov homology carries a commuting action of the symmetric group . One therefore obtains a 'knotted' Schur-Weyl representation that agrees with classical Schur-Weyl duality when is the Seifert-framed unknot.",

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AU - Wehrli, Stephan M.

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N2 - Let be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of , the exterior current algebra of . When is an -framed -cable of a knot , its sutured annular Khovanov homology carries a commuting action of the symmetric group . One therefore obtains a 'knotted' Schur-Weyl representation that agrees with classical Schur-Weyl duality when is the Seifert-framed unknot.

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Annular Khovanov homology and knotted Schur-Weyl representations

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