Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

作     者：Zhan Qiang BAI Wei XIAO 

作者机构：School of Mathematical SciencesSoochow UniversitySuzhou 215006P.R.China College of Mathematics and statisticsShenzhen Key Laboratory of Advanced Machine Learning ApplicationsShenzhen UniversityShenzhen 518060P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第11期

页      面：1854-1860页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Science Foundation of China(Grant No.11601394) supported by the National Science Foundation of China(Grant No.11701381) Guangdong Natural Science Foundation(Grant No.2017A030310138) 

主　　题：Gelfand–Kirillov dimension generalized Verma module reducibility 

摘      要：The Gelfand–Kirillov dimension is an invariant which can measure the size of infinitedimensional 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.