3 A pr 2 00 3 Classification of Quasifinite Modules over the Lie Algebras of Weyl Type
نویسنده
چکیده
For a nondegenerate additive subgroup Γ of the n-dimensional vector space IF over an algebraically closed field IF of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type W(Γ, n) spanned by all differential operators uD1 1 · · ·D mn n for u ∈ IF [Γ] (the group algebra), and m1, ...,mn ≥ 0, where D1, ...,Dn are degree operators. In this paper, it is proved that an irreducible quasifinite W(ZZ, 1)-module is either a highest or lowest weight module or else a module of the intermediate series; furthermore, a classification of uniformly bounded W(ZZ, 1)modules is completely given. It is also proved that an irreducible quasifinite W(Γ, n)-module is a module of the intermediate series and a complete classification of quasifinite W(Γ, n)-modules is also given, if Γ is not isomorphic to ZZ.
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