Duality on Fock spaces and combinatorial energy functions

We generalize in a combinatorial way the notion of the affine energy function of type $A$ to the case of a more general class of modules over a general linear Lie superalgebra $\mathfrak{g}$ based on a Howe duality of type $(\mathfrak{g},{\mathfrak{g}\mathfrak{l}}_n)$ on various Fock spaces.