FEIGIN-FUKS REPRESENTATIONS FOR NONEQUIVALENT ALGEBRAS OF N=4 SUPERCONFORMAL SYMMETRY

The N = 4 SU(2)(k) superconformal algebra has the global automorphism of SO(4) approximate to SU(2) x SU(2) with the left factor as the Kac- Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by rho corresponding to the conjugate classes of the outer automorphism group SO(4)/SU(2) = SU(2) are obtained a la Schwim mer and Seiberg. We construct Feigin-Fuks representations with the rho parameter embedded for the infinite set of the N = 4 nonequivalent al gebras. In our construction the extended global SU(2) algebras labeled by rho are self-consistently represented by fermion fields with appro priate boundary conditions.