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Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields (2102.09064v1)
Published 17 Feb 2021 in math.RT
Abstract: Let ${\mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${\mathcal W}_n$-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 associated with the de Rham complex on $\mathbb Cn$.