N = 2 affine superalgebras and Hamiltonian reduction in N = 2 superspace

We construct N = 2 affine current algebras for the superalgebras sl(n|n - 1)⁽¹⁾ in terms of N = 2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction in N = 2 superspace at the classical level. We consider in detail the simplest case of N = 2 sl(2|1)⁽¹⁾ and show how N = 2 superconformal algebra in N = 2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case of N = 2 sl(3 2)⁽¹⁾, we find two new extended N = 2 superconformal algebras in a manifestly supersymmetric N = 2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively, u(2|1) and u(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how the N = 2 superfield formulations of N = 2 W₃, and N = 2 W⁽²⁾₃ superconformal algebras come out in this framework, as well as some unusual extended N = 2 superconformal algebras containing constrained N = 2 stress tensor and/or spin 0 supercurrents.