Annular Khovanov homology and knotted Schur-Weyl representations

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.