Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields-Reference-Cited by-同舟云学术

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

Published:2022-09-29 Issue:792 Volume:2022 Page:93-114
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Grantcharov Dimitar¹,Serganova Vera²

Affiliation:

1. Department of Mathematics , University of Texas at Arlington , Arlington , TX 76019 , USA

2. Department of Mathematics , University of California at Berkeley , Berkeley , CA 94720 , USA

Abstract

Abstract Let 𝒲 n

{{\mathcal{W}}_{n}}

be the Lie algebra of polynomial vector fields. We classify simple weight 𝒲 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 associated with the de Rham complex on ℂ n

{\mathbb{C}^{n}}

Funder

National Science Foundation

Simons Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2022-0053/pdf

Reference21 articles.

1. Y. Billig and V. Futorny, Classification of irreducible representations of Lie algebra of vector fields on a torus, J. reine angew. Math. 720 (2016), 199–216.

2. A. Cavaness and D. Grantcharov, Bounded weight modules of the Lie algebra of vector fields on ℂ 2 \mathbb{C}^{2} , J. Algebra Appl. 16 (2017), no. 12, Article ID 1750236.

3. I. Dimitrov, O. Mathieu and I. Penkov, On the structure of weight modules, Trans. Amer. Math. Soc. 352 (2000), no. 6, 2857–2869.

4. B. L. Feĭgin and D. B. Fuks, Homology of the Lie algebra of vector fields on the line, Funct. Anal. Appl. 14 (1980), 201–212.

5. S. L. Fernando, Lie algebra modules with finite-dimensional weight spaces. I, Trans. Amer. Math. Soc. 322 (1990), no. 2, 757–781.

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