Realizations of Affine Lie Algebra A_^(1) at Negative Levels

Abstract

A realization of the affine Lie algebra $A_1^{(1)}$ and the relevant $Z$-algebra at negative level $-k$ is given in terms of parafermions. This generalizes the recent work on realization of the affine Lie algebra at the critical level.

12 pages. Paper presented at Conference on Algebra, Geometry and Mathematical Physics held at the University of Haute Alsace, France, October 2011. A. Makhlouf et al. (eds.), Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics & Statistics 85, Springer-Verlag, Berlin Heidelberg, 2014

References in corpus (4)

• Lie superalgebras and irreducibility of A_1^(1)-modules at the critical level
• Twisted Parafermions
• $A_2^{(2)}$ Parafermions: A New Conformal Field Theory
• Realization of \hat{sl}_2(C) at the Critical Level