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Acta Mathematica Sinica, English Series

, Volume 35, Issue 11, pp 1854–1860 | Cite as

Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

  • Zhan Qiang Bai
  • Wei XiaoEmail author
Article
  • 33 Downloads

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.

Keywords

Gelfand-Kirillov dimension generalized Verma module reducibility 

MR(2010) Subject Classification

22E47 17B10 17B20 

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Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouP. R. China
  2. 2.College of Mathematics and statistics, Shenzhen Key Laboratory of Advanced Machine Learning and ApplicationsShenzhen UniversityShenzhenP. R. China

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