Realizations of Affine Lie Algebra A_^(1) at Negative Levels
  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. 
Jilan Dong, Naihuan Jing
math.QA hep-th