FOCK REPRESENTATIONS AND BRST COHOMOLOGY IN SL(2) CURRENT-ALGEBRA

We investigate the structure of the Fock modules over A1(1) introduced by Wakimoto. We show that irreducible highest weight modules arise as degree zero cohomology groups in a BRST-like complex of Fock modules. Chiral primary fields are constructed as BRST invariant operators acting on Fock modules. As a result, we obtain a free field representation of correlation functions of the SU(2) WZW model on the plane and on the torus. We also consider representations of fractional level arising in Polyakov's 2 D quantum gravity. Finally, we give a geometrical, Borel-Weil-like interpretation of the Wakimoto construction. © 1990 Springer-Verlag.