On the Boson-Fermion Correspondence for Factorial Schur Functions

2025/02/05 by Bump, Daniel, Hardt, Andrew, Scrimshaw, Travis
#Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.02841

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.

Related

• Factorial Fock free fermions
• A combinatorial generalization of the Boson-Fermion correspondence
• Boson-fermion correspondence from factorization spaces
• Functional Representations for Fock Superalgebras
• Generating functions of dual K-theoretic P- and Q-functions and boson-fermion correspondence