On the Boson-Fermion Correspondence for Factorial Schur Functions

TL;DR

This paper provides an algebraic proof of the boson-fermion correspondence for factorial Schur functions, avoiding analytic assumptions and connecting to Lie algebra representations.

Contribution

It offers a new algebraic proof of the deformed boson-fermion Fock space construction for factorial Schur functions, extending previous analytic approaches.

Findings

Algebraic proof of the boson-fermion correspondence for factorial Schur functions

Connection between the construction and representations of infinite rank Lie algebras

Recovery of factorial Schur functions through specialization and shifting

Abstract

We give an algebraic (non-analytic) proof of the deformed boson-fermion Fock space construction of Molev's double supersymmetric Schur functions, among other results, from our previous paper. In other words, we make no assumptions on the variables and parameters. By specializing to a finite number of variables and shifting parameters, we recover the factorial Schur functions. Furthermore, we realize the bosonic construction through a representation of a completion of the infinite rank general linear Lie algebra.