ON THE HOMOLOGICAL CONSTRUCTION OF CASIMIR ALGEBRAS

We propose a BRST (homological) construction of the Casimir extended conformal algebras by quantizing a classical observation of Drinfeld and Sokolov. We give the explicit expression for the Virasoro generators and compute the discrete series of the Casimir algebras. The unitary subseries agrees with that of the coset construction for the case of simply laced algebras. With the help of a free-field realization of the affine algebra, we compute the BRST cohomology of this system with coefficients in a Fock module. This allows us to generalize and prove a conjecture of Bershadsky and Ooguri. © 1990.