Realization of \hat{sl}_2(C) at the Critical Level

TL;DR

This paper constructs an explicit realization of the affine Lie algebra sl_2(C) at the critical level using bosons and parafermions, and explores its associated algebra representations.

Contribution

It introduces a novel explicit construction of sl_2(C) at the critical level with a new representation framework involving bosons and parafermions.

Findings

Explicit realization of sl_2(C) at critical level

Representation of Lepowsky-Wilson Z-algebra on tensor spaces

Connection between bosonic fields and semi-infinite wedge products

Abstract

An explicit realization of the affine Lie algebra \hat{sl}_2(C) at the critical level is constructed using a mixture of bosons and parafermions. Subsequently a representation of the associated Lepowsky-Wilson Z-algebra is given on a space of the tensor product of bosonic fields and certain semi-infinite wedge products.