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 sl(2,C), generalizing the well-known structure on the harmonic forms of compact Kähler manifolds. Some topological implications are deduced. [ABSTRACT FROM AUTHOR]