Unitary representations of some infinite-dimensional Lie algebras motivated by string theory on AdS(3)

We consider some unitary representations of infinite-dimensional Lie algebr as motivated by string theory on AdS(3). These include examples of two kind s: the A,D,E type affine Lie algebras and the N = 4 superconformal algebra. The first presents a new construction for free field representations of af fine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for str ing theory on AdS(3) exists. (C) 1999 Elsevier Science B.V. All rights rese rved.