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Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

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Abstract

The Gelfand-Kirillov dimension is an invariant which can measure the size of infinite-dimensional algebraic structures. In this article, we show that it can also measure the reducibility of scalar generalized Verma modules. In particular, we use it to determine the reducibility of scalar generalized Verma modules associated with maximal parabolic subalgebras in the Hermitian symmetric case.

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Acknowledgements

We would like to thank the anonymous referees for valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Soochow University, Suzhou, 215006, P. R. China

    Zhan Qiang Bai

  2. College of Mathematics and statistics, Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen, 518060, P. R. China

    Wei Xiao

Authors
  1. Zhan Qiang Bai
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  2. Wei Xiao
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Corresponding author

Correspondence to Wei Xiao.

Additional information

The first author is supported by the National Science Foundation of China (Grant No. 11601394); the second author is supported by the National Science Foundation of China (Grant No. 11701381) and Guangdong Natural Science Foundation (Grant No. 2017A030310138)

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Bai, Z.Q., Xiao, W. Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules. Acta. Math. Sin.-English Ser. 35, 1854–1860 (2019). https://doi.org/10.1007/s10114-019-9069-y

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  • DOI: https://doi.org/10.1007/s10114-019-9069-y

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