Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules
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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.
KeywordsGelfand-Kirillov dimension generalized Verma module reducibility
MR(2010) Subject Classification22E47 17B10 17B20
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We would like to thank the anonymous referees for valuable comments and suggestions.
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