Classification of quasifinite representations of a Lie algebra related to Block type

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A well-known theorem of Mathieu's states that a Harish-chandra module over the Virasoro algebra is either a highest weight module, a lowest weight module or a module of the intermediate series. It is proved in this paper that an analogous result also holds for the Lie algebra related to Block type, with basis L,ᵢ,C|a,i∈, i≥0 and relations [L,ᵢ,L,ⱼ]=((i+1)-(j+1))L₊,ᵢ₊ⱼ+₊,₀ᵢ₊ⱼ,₀³-/6C, [C,L,ᵢ]=0.Namely, an irreducible quasifinite -module is either a highest weight module, a lowest weight module or a module of the intermediate series.