Irreducible Wakimoto-like Modules for the Lie Superalgebra D(2,1;α)  

作　　者：Jin CHENG Zi Ting ZENG 

机构地区：[1]School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, P. R. China [2]School of Mathematical Science, Beijing Normal University, Beijing 100875, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第10期1578-1588,共11页数学学报（英文版）

基　　金：Supported by NSF of China(Grant Nos.11701340 and 11271043)

摘　　要：By using the idea of Wakimoto＇s free field, we construct a class of representations for the Lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter A. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact. the representation is irreducible if and only if the parameter ,λ satisfies （λ＋m）（λ-1＋α/αm）≠0 for any m∈Z＋.By using the idea of Wakimoto＇s free field, we construct a class of representations for the Lie superalgebra D（2, 1; α） on the tensor product of a polynomial algebra and an exterior algebra involving one parameter A. Then we obtain the necessary and sufficient condition for the representations to be irreducible. In fact. the representation is irreducible if and only if the parameter ,λ satisfies （λ＋m）（λ-1＋α/αm）≠0 for any m∈Z＋.

关 键 词：Lie superalgebra REPRESENTATION Wakimoto＇s free field 

分 类 号：O152.5[理学—数学]