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

Abstract

In this paper, we introduce a family of functors denoted as Fb, which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors. Our constructed functors recover specific irreducible modules over N = 2 superconformal algebras, including intermediate series and U(h)-free modules. Additionally, we show that our constructed functors yield several new irreducible modules for N = 2 superconformal algebras.