QUANTUM GROUP-STRUCTURE IN THE FOCK SPACE RESOLUTIONS OF SL-OR-(N) REPRESENTATIONS

We describe a complex of Wakimoto-type Fock space modules for the affine Kac-Moody algebra {Mathematical expression}. The intertwining operators that build the complex are obtained from contour integrals of so-called screening operators. We show that a quantum group structure underlies the algebra of screening operators. This observation greatly facilitates the explicit determination of the intertwiners. We conjecture that the complex provides a resolution of an irreducible highest weight module in terms of Fock spaces. © 1990 Springer-Verlag.