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

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.

12 pages

References in corpus (1)

• Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level

Cited by in corpus (2)

• Realizations of Affine Lie Algebra A_^(1) at Negative Levels
• On principal realization of modules for the affine Lie algebra $A_1^{(1)}$ at the critical level