A New Functor from D_5-Mod to E_6-Mod

作     者：Xiao Ping XU 

作者机构：Hua Loo-Keng Key Mathematical LaboratoryInstitute of MathematicsAcademy of Mathematics & System SciencesChinese Academy of Sciences 

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

年 卷 期：2016年第32卷第8期

页      面：867-892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 NSFC(Grant Nos.11171324 and 11321101) 

主　　题：Simple Lie algebra of type E6 simple Lie algebra of type Ds module category functor,irreducibility 

摘      要：We find a new representation of the simple Lie algebra of type E6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen＇s idea of mixed product, we construct a new functor from Ds-Mod to E6-Mod. A condition for the functor to map a finite-dimensional irreducible Ds-module to an infinite-dimensional irreducible E6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant＇s characteristic identities plays a key role.