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 $G\oplus sl(2)$. At the classical level we obtain generic formulas for the Poisson bracket structure of the algebra. At the quantum level 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 $sl(2)\oplus sp(2N)$ extended superconformal algebra from the Lie superalgebra $osp(4|2N)$. We also discuss the screening operators of the algebra and the structure of singular vectors in the free field representation.