FREE-FIELD REPRESENTATIONS OF EXTENDED SUPERCONFORMAL ALGEBRAS

We study the classical and quantum G extended superconformal algebras from the hamiltonian reduction of affine Lie superalgebras, with even subalgebras G + sl(2). At the classical level we obtain generic formul as for the Poisson bracket structure of the algebra. At the quantum le vel we get free field (Feigin-Fuchs) representations of the algebra by using the BRST formalism and the free field realization of the affine Lie superalgebra. In particular we get the free field representation of the sl(2) + sp(2N) extended superconformal algebra from the Lie sup eralgebra osp(4\2N). We also discuss the screening operators of the al gebra and the structure of singular vectors in the free field represen tation.