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

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We introduce a class of infinite Lie conformal superalgebras S(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 NS if p=−1, where NS is a Neveu-Schwarz conformal subalgebra of S(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.