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

作     者：Zhan Qiang BAI Jing JIANG Zhan Qiang BAI;Jing JIANG

作者机构：School of Mathematical SciencesSoochow UniversitySuzhou 215006P.R.China E-mail:zqbai@*** jjsd6514@*** 

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

年 卷 期：2024年第40卷第3期

页      面：658-706页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

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)。 

主　　题：Generalized Verma module Gelfand-Kirillov dimension Young tableau 

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.