Extensions of modules over supercurrent conformal algebras

In the papers [2] and [3], Cheng, Kac and Wakimoto classify extensions between finite conformal modules over the Virasoro, the Neveu-Schwarz, the current and the semidirect sum of the Virasoro and the current conformal algebras. In this paper, we continue their program and classify extensions between two finite irreducible modules over the supercurrent conformal algebras. The method here as in [3] is based on the theory of conformal modules [1] and the techniques developed in [2].