  We define a new family of commuting operators $F_k$ in Khovanov-Rozansky link
homology, similar to the action of tautological classes in cohomology of
character varieties. We prove that $F_2$ satisfies ``hard Lefshetz property"
and hence exhibits the symmetry in Khovanov-Rozansky homology conjectured by
Dunfield, Gukov and Rasmussen.
