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

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

31 Citations (Scopus)

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

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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 - Grigsby, J. Elisenda

AU - Licata, Anthony M.

AU - Wehrli, Stephan M.

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Y1 - 2018/3/1

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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85041626311

U2 - 10.1112/S0010437X17007540

DO - 10.1112/S0010437X17007540

M3 - Article

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SP - 459

EP - 502

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 3

ER -

Annular Khovanov homology and knotted Schur-Weyl representations

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