On classification of quasifinite representations of two classes of Lie superalgebras of block type

摘要

Motivated by a well-known theorem of Mathieu's on Harish-Chandra modules over the Virasoro algebra and its super version, we show that an irreducible quasifinite module over two classes of Lie superalgebras ?(q) of Block type is either a highest or lowest weight module or else a module of the intermediate series if q-1. For such a module over ?(-1), we give a rough classification.