Short Distance Expansion from the Dual Representation of Infinite   Dimensional Lie Algebras
  We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N-extended supersymmetric GR Virasoro algebra. 
S. James Gates Jr, W.D. Linch III, J. Phillips and V.G.J. Rodgers