Duality on Fock spaces and combinatorial energy functions

TL;DR

This paper extends the combinatorial understanding of affine energy functions from type A to broader modules over general linear Lie superalgebras, utilizing Howe duality on Fock spaces.

Contribution

It introduces a combinatorial generalization of affine energy functions for modules over Lie superalgebras using Howe duality.

Findings

Generalized affine energy functions to Lie superalgebra modules

Connected combinatorial models with Howe duality

Enhanced understanding of Fock space representations

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.