Fundamental quasisymmetric functions in superspace

TL;DR

This paper introduces fundamental quasisymmetric functions in superspace, extending classical concepts to include anticommuting variables, and explores their algebraic properties and relations to Schur functions.

Contribution

It generalizes fundamental quasisymmetric functions to superspace and details their algebraic structure and connection to Schur functions.

Findings

Derived the product, coproduct, and antipode actions in superspace

Extended Schur function expansions to superspace

Established algebraic properties of superspace quasisymmetric functions

Abstract

The fundamental quasisymmetric functions in superspace are a generalization of the fundamental quasisymmetric functions involving anticommuting variables. We obtain the action of the product, coproduct, and antipode on the fundamental quasisymmetric functions in superspace. We also extend to superspace the well known expansion of the Schur functions in terms of fundamental quasisymmetric functions.