Classification of Finite Irreducible Conformal Modules over N = 2 Lie Conformal Superalgebras of Block Type

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We introduce the N = 2 Lie conformal superalgebras \({\frak {K}}(p)\) 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 M over K2 if p = − 1 and M has rank (2 + 2), where K2 is an N = 2 conformal subalgebra of \({\frak {K}}(p)\). As a byproduct, we obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal superalgebras \({\frak k}(n)\) for n ≥ 1. Composition factors of all the involved reducible conformal modules are also determined.