Bounded weight modules of the Lie algebra of vector fields on ${\mathbb C}^2$

Andrew Cavaness; Dimitar Grantcharov

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arXiv · 1611.01821

Bounded weight modules of the Lie algebra of vector fields on ${\mathbb C}^2$

Andrew Cavaness·Dimitar Grantcharov

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Abstract

We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification we introduce a new family of generalized tensor $W_n$-modules. Our classification result is an important step in the classification of all simple weight $W_n$-modules with finite weight multiplicities.

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BibTeX RIS

Andrew Cavaness, Dimitar Grantcharov. 2017-06-15. Bounded weight modules of the Lie algebra of vector fields on ${\mathbb C}^2$. https://arxiv.org/abs/1611.01821

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