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

We introduce the N = 2 Lie conformal superalgebras K(p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\frak {K}}(p)$\end{document} 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 K(p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\frak {K}}(p)$\end{document}. As a byproduct, we obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal superalgebras k(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\frak k}(n)$\end{document} for n ≥ 1. Composition factors of all the involved reducible conformal modules are also determined.