Generalized duality for kk-forms

We give the definition of a duality that is applicable to arbitrary kk-forms. The operator that defines the duality depends on a fixed form ΩΩ. Our definition extends in a very natural way the Hodge duality of nn-forms in 2n2n dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where ΩΩ is invariant with respect to a subalgebra of so(V)so(V). Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.

► The definition of generalized duality for arbitrary kk-forms is given. ► Classical duality relations are shown to be subcases. ► The duality provides a decomposition of the space of kk-forms. ► Examples of Lie algebra invariant forms are discussed. ► The duality is applied to democratic forms with discrete symmetry.