Whittaker Modules for the Derivation Lie Algebra of Torus with Two Variables  

作　　者：Hai Feng LIAN Xiu Fu ZHANG 

机构地区：[1]Department of Mathematics,Fujian Agriculture and Forestry University,Fuzhou 350002,P.R.China [2]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2016年第10期1177-1188,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11571145 and 11271165);the Youth Foundation of National Natural Science Foundation of China(Grant Nos.11101350 and 11302052);the Natural Science Foundation of Fujian Province(Grant No.2010J05001)

摘　　要：Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module We of type φ. We obtain all Whittaker vectors and submodules of We. Moreover, all simple Whittaker L-modules of type φ are determined.Let L be the derivation Lie algebra of C[t1^±1 , t2^±1 ]. Given a triangle decomposition L = L＋ η ＋ L-, we define a nonsingular Lie algebra homomorphism φ ： L＋ → C and the universal Whittaker L-module We of type φ. We obtain all Whittaker vectors and submodules of We. Moreover, all simple Whittaker L-modules of type φ are determined.

关 键 词：Whittaker vector Whittaker module simple module derivation Lie algebra 

分 类 号：O152.5[理学—数学]