Gelfand-Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie Algebras  

作　　者：Zhan Qiang BAI Jing JIANG 

机构地区：[1]School of Mathematical Sciences,Soochow University,Suzhou 215006,P.R.China E-mail:[e-mail] [e-mail]

出　　处：《Acta Mathematica Sinica,English Series》2024年第3期658-706,共49页数学学报（英文版）

基　　金：Supported by the National Science Foundation of China(Grant No.12171344);the National Key R&D Program of China(Grant Nos.2018YFA0701700 and 2018YFA0701701)。

摘　　要：Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module.In this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.

关 键 词：Generalized Verma module Gelfand-Kirillov dimension Young tableau 

分 类 号：O152.5[理学—数学]