Duality on Fock spaces and combinatorial energy functions

Abstract

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 $(\mathfrak{g},{\mathfrak{gl}}_n)$ on various Fock spaces.

26 pages, minor revision, to appear in Journal of Combinatorial Theory, Series A