Comments related to infinite wedge representations

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.

arXiv commentFinal Version. Published in by C. R. Math. Acad. Sci. Soc. R. Can (2017)