Harmonic symmetries for Hermitian manifolds
Complex manifolds with compatible metric have a naturally defined subspace of harmonic differential forms that satisfy Serre, Hodge, and conjugation duality, as well as hard Lefschetz duality. This last property follows from a representation of 

 
 
 
 s
 l
 
 (
 2
 ,
 
 C
 
 )
 
 \mathfrak {sl}(2,\mathbb {C})
 

, generalizing the well-known structure on the harmonic forms of compact Kähler manifolds. Some topological implications are deduced.