Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules |
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| Authors: | Zhan Qiang Bai Wei Xiao |
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| Institution: | 1.School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China;2.College of Mathematics and statistics, Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen 518060, P. R. China |
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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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| Keywords: | Gelfand-Kirillov dimension generalized Verma module reducibility |
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