Classification of finite irreducible conformal modules over Lie conformal superalgebras of Block type

We introduce a class of infinite Lie conformal superalgebras G(p) of Block type, and classify their finite irreducible conformal modules for any nonzero parameter p. In particular, we show that such a conformal module admits a nontrivial extension of a finite conformal module over NG if p = -1, where NG is a Neveu-Schwarz conformal subalgebra of G(p). As a byproduct, we also obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal superalgebras s(n) for n >= 1. (C) 2019 Elsevier Inc. All rights reserved.