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

2021/02/17 by Grantcharov, Dimitar, Serganova, Vera · 2 citations
#17B10 #17B66 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2102.09064

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.

Cited by

• Classification of Simple Cuspidal Modules over Nongraded Witt Lie Algebras
• Simple smooth modules over the Lie algebras of polynomial vector fields

Related

• Classification of simple bounded weight modules of the Lie algebra of vector fields on \Cⁿ
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