一类单李代数的广义Verma模  

Generalized Verma modules on a class of simple Lie algebras

作　　者：张瑾怡 申冉[1] 陈雨露 ZHANG Jinyi;SHEN Ran;CHEN Yulu(College of Science,Donghua University,Shanghai 201620,China)

机构地区：[1]东华大学理学院,上海201620

出　　处：《东华大学学报（自然科学版）》2024年第5期176-180,共5页Journal of Donghua University(Natural Science)

基　　金：中央高校基本科研业务费专项资金(2232022G-13)

摘　　要：广义Verma模作为Verma模的自然推广,其结构及分类对研究经典Verma模的结构性质具有重要作用。为得到单李代数的一些新的表示,主要讨论由sl(2,C)诱导的B_(2)的广义Verma模的不可约性。从B_(2)型李代数g的根与根向量出发,取定g的一组基,利用李积关系及其Cartan分解,由sl(2,C)的Whittaker模,诱导出B_(2)型李代数的广义Verma模,通过对该广义Verma模的生成向量进行讨论,证明了该广义Verma模是不可约模。Generalized Verma modules are the natural generalization of Verma modules.To get some new representations of simple Lie algebras,we discussed the irreducibility of the generalized Verma module of B_(2)induced from sl(2,C).We The study started from the roots and the root vectors of the Lie algebra g of type B_(2).A group of bases of g was given.We used their Lie product relations,the triangular decomposition of g and the Whittaker module of sl(2,C)to induce the generalized Verma module.The irreducibility of the generalized Verma module is determined by discussing the generating vectors.

关 键 词：广义Verma模 单模 Whittaker模 B_(2)型李代数 

分 类 号：O151.2[理学—数学]