Comments related to infinite wedge representations

TL;DR

This paper explores the infinite wedge representation's connection to loop algebras, providing an elementary proof of the boson-fermion correspondence using combinatorial methods and the Murnaghan-Nakayama rule.

Contribution

It offers a new combinatorial approach to understanding the infinite wedge representation and provides an elementary proof of the boson-fermion correspondence.

Findings

Established the relation between infinite wedge representation and loop algebra extension.

Provided an elementary combinatorial proof of the boson-fermion correspondence.

Connected combinatorial constructions with algebraic structures in representation theory.

Abstract

We study the infinite wedge representation and show how it is related to the universal extension of $g[t,t^{-1}]$ the loop algebra of a complex semi-simple Lie algebra $g$. We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction with partitions combined with an application of the Murnaghan-Nakayama rule.