Abstract
In this paper, an explicit determinant formula is given for the Verma modules over the Lie algebra W(2, 2). We construct a natural realization of certain vaccum module for the algebra W(2, 2) via theWeyl vertex algebra. We also describe several results including the irreducibility, characters and the descending filtrations of submodules for the Verma module over the algebra W(2, 2).
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11271056, 11671056 and 11101030), National Science Foundation of Jiangsu (Grant No. BK20160403), National Science Foundation of Zhejiang (Grant Nos. LQ12A01005 and LZ14A010001), National Science Foundation of Shanghai (Grant No. 16ZR1425000), Beijing Higher Education Young Elite Teacher Project and Morning- side Center of Mathematics. The authors thank the two anonymous reviewers for their helpful comments and suggestions.
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Jiang, W., Pei, Y. & Zhang, W. Determinant formula and a realization for the Lie algebra W (2, 2). Sci. China Math. 61, 685–694 (2018). https://doi.org/10.1007/s11425-016-9046-1
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DOI: https://doi.org/10.1007/s11425-016-9046-1