J. Elisenda Grigsby, Anthony M. Licata, Stephan M. Wehrli
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.
Journal: Compositio Mathematica. 154, 3, p. 459-502.
DOI: 10.1112/S0010437X17007540