Generalized projective representations for sl(n+1) | |
Zhao, Yufeng1; Xu, Xiaoping2 | |
2011-02-15 | |
发表期刊 | JOURNAL OF ALGEBRA |
ISSN | 0021-8693 |
卷号 | 328期号:1页码:132-154 |
摘要 | It is well known that n-dimensional projective group gives rise to a non-homogeneous representation of the Lie algebra sl(n + 1) on the polynomial functions of the projective space. Using Shen's mixed product for Witt algebras (also known as Larsson functor), we generalize the above representation of sl(n + 1) to a non-homogeneous representation on the tensor space of any finite-dimensional irreducible gl(n)-module with the polynomial space. Moreover, the structure of such a representation is completely determined by employing projection operator techniques and well-known Kostant's characteristic identities for certain matrices with entries in the universal enveloping algebra. In particular, we obtain a new one parameter family of infinite-dimensional irreducible sl(n + 1)-modules. which are in general not highest-weight type, for any given finite-dimensional irreducible sl(n)-module. The results could also be used to study the quantum field theory with the projective group as the symmetry. (C) 2010 Elsevier Inc. All rights reserved. |
关键词 | Special linear Lie algebra Representation of Lie algebra Characteristic identities |
DOI | 10.1016/j.jalgebra.2010.07.009 |
语种 | 英语 |
资助项目 | NSFC[10701002] |
WOS研究方向 | Mathematics |
WOS类目 | Mathematics |
WOS记录号 | WOS:000286447400008 |
出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/13108 |
专题 | 数学所 |
通讯作者 | Zhao, Yufeng |
作者单位 | 1.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Hua Loo Keng Key Math Lab, Beijing 100190, Peoples R China |
推荐引用方式 GB/T 7714 | Zhao, Yufeng,Xu, Xiaoping. Generalized projective representations for sl(n+1)[J]. JOURNAL OF ALGEBRA,2011,328(1):132-154. |
APA | Zhao, Yufeng,&Xu, Xiaoping.(2011).Generalized projective representations for sl(n+1).JOURNAL OF ALGEBRA,328(1),132-154. |
MLA | Zhao, Yufeng,et al."Generalized projective representations for sl(n+1)".JOURNAL OF ALGEBRA 328.1(2011):132-154. |
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