Conformal oscillator representations of orthogonal Lie algebras

作     者：XU XiaoPing 

作者机构：HUA Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2016年第59卷第1期

页      面：37-48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 National Natural Science Foundation of China(Grant Nos.11171324 and 11321101) 

主　　题：orthogonal Lie algebra differential operator oscillator representation irreducible module poly- nomial algebra exponential-polynomial function 

摘      要：The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o（n ＋ 2, C）. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a^→∈ C^n, we prove that the space forms an irreducible o（n ＋ 2, C）-module for any c ∈ C if a^→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o（n＋2, C） on the polynomial algebra in n variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight o（n ＋2, C）-module with finite-dimensional weight subspaces if c Z/2.