Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields

Abstract

AbstractLet𝒲n{{\mathcal{W}}_{n}}be the Lie algebra of polynomial vector fields. We classify simple weight𝒲n{{\mathcal{W}}_{n}}-modulesMwith finite weight multiplicities. We prove that every such nontrivial moduleMis either a tensor module or the unique simple submodule in a tensor module associated with the de Rham complex onℂn{\mathbb{C}^{n}}.