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Abstract Let đť’˛ n {{\mathcal{W}}_{n}} be the Lie algebra of polynomial vector fields.We classify simple weight đť’˛ n {{\mathcal{W}}_{n}} -modules M with finite weight multiplicities. We prove that every such nontrivial module M is either a tensor module or the unique simple submodule in a tensor module associatedwith the de Rham complex on â„‚ n {\mathbb{C}^{n}} .more » « less
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null (Ed.)We describe all blocks of the category of finite-dimensional q(3)-supermodules by providing their extension quivers. We also obtain two general results about the representation of q(n): we show that the Ext quiver of the standard block of q(n) is obtained from the principal block of q(n-1) by identifying certain vertices of the quiver and prove a virtual BGG-reciprocity for q(n). The latter result is used to compute the radical filtrations of q(3) projective covers.more » « less
