Annular Khovanov homology and knotted Schur–Weyl representations. (28th November 2017) - Grigsby, J. Elisenda; Licata, Anthony M.; Wehrli, Stephan M.
Abstract : Let LA× I be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of sl_2(), the exterior current algebra of sl_2 . When L is an m -framed n -cable of a knot KS^3, 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.