Irreducible modules over N=2 superconformal algebras from algebraic D-modules

In this paper, we introduce a family of functors denoted ℱ_b that act on algebraic D-modules and generate modules over N=2 superconformal algebras. We prove these functors preserve irreducibility for all values of b, with a few clear exceptions described. We also establish necessary and sufficient conditions to determine when two such functors are naturally isomorphic. Applying ℱ_b to N=1 super-Virasoro algebras recovers the functors previously introduced in . Our new functors also facilitate the recovery of specific irreducible modules over N=2 superconformal algebras, including intermediate series and U(𝔥)-free modules. Additionally, our constructed functors produce several new irreducible modules for N=2 superconformal algebras.