Science China Mathematics

, Volume 61, Issue 4, pp 685–694 | Cite as

Determinant formula and a realization for the Lie algebra W (2, 2)

  • Wei Jiang
  • Yufeng Pei
  • Wei Zhang


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).


Lie algebra Verma module highest weight representation W(2, 2) algebra vertex algebra 


17B68 17B69 


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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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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsChangshu Institute of TechnologyChangshuChina
  2. 2.Department of MathematicsShanghai Normal UniversityShanghaiChina
  3. 3.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina

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