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

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Abstract

Let W +n be the Lie algebra of vector fields on ℂn. In this paper, we classify all simple bounded weight modules. Any such module is isomorphic to the simple quotient of a tensor module F(P, M) = P ⊗ M for a simple weight module P over the Weyl algebra \(K_n^ + = \mathbb{C}\left[ {{t_1}, \ldots ,{t_n},{\partial \over {\partial {t_1}}}, \ldots ,{\partial \over {\partial {t_n}}}} \right]\) and a finite-dimensional simple \({\mathfrak{g}\mathfrak{l}_n}\left(\mathbb{C} \right)\) module M.

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Acknowledgement

This work is partially supported by NSF of China (Grants 11471233, 11771122,11801390, 11971440). The authors would like to thank the referee for his/her nice suggestions.

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  1. Department of Mathematics, Soochow University, Suzhou, P. R. China

    Yaohui Xue & Rencai Lü

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  1. Yaohui Xue
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  2. Rencai Lü
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Correspondence to Rencai Lü.

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Xue, Y., Lü, R. Classification of simple bounded weight modules of the Lie algebra of vector fields on ℂn. Isr. J. Math. 253, 445–468 (2023). https://doi.org/10.1007/s11856-022-2371-x

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  • DOI: https://doi.org/10.1007/s11856-022-2371-x

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