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Tensor modules over Witt superalgebras

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Abstract

In this paper, we study the tensor module P ⊗ M over the Witt superalgebra W +m,n (resp. Wm,n), where P is a simple module over the Weyl superalgebra K +m,n (resp. Km,n) and M is a simple weight module over the general linear Lie superalgebra \(\mathfrak{g}\mathfrak{l}\left( {m,n} \right)\). We obtain the necessary and sufficient conditions for P ⊗ M to be simple, and determine all the simple subquotients of P ⊗ M when it is not simple. All the work leads to the completion of some classification problems on the weight representation theories of W +m,n and Wm,n.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11971440, 11801390 and 11871052). The authors thank Professor Rencai Lü for formulating the problem and his help in preparation of this paper, and thank the referees for their helpful suggestions and comments.

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Authors and Affiliations

  1. Department of Mathematics, Soochow University, Suzhou, 215021, China

    Yaohui Xue

  2. School of Mathematics, Tianjin University, Tianjin, 300354, China

    Yan Wang

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  1. Yaohui Xue
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  2. Yan Wang
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Correspondence to Yan Wang.

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Xue, Y., Wang, Y. Tensor modules over Witt superalgebras. Sci. China Math. 66, 1429–1448 (2023). https://doi.org/10.1007/s11425-021-2004-5

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  • DOI: https://doi.org/10.1007/s11425-021-2004-5

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