Conformal oscillator representations of orthosymplectic Lie superalgebras

doi:10.1016/j.jpaa.2020.106530

CSpace

	Conformal oscillator representations of orthosymplectic Lie superalgebras
	Xu, Xiaoping 1,2
	2021-03-01
发表期刊	JOURNAL OF PURE AND APPLIED ALGEBRA
ISSN	0022-4049
卷号	225 期号:3 页码:24
摘要	In this paper, we generalize the one-parameter (c) family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie superalgebras, and determine the irreducible condition. Letting these supersymmetric differential operators act on the space of supersymmetric exponential-polynomial functions that depend on a parametric vector (a)over-right-arrow is an element of C-n, we prove that the space forms an irreducible osp(n + 2 vertical bar 2m)-module for any c is an element of C if (a)over-right-arrow is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general supersymetric differential operator representations of osp(n + 2 vertical bar 2m) on the polynomial algebra l in n m supersymetric variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight osp(n + 2 vertical bar 2m)-module with finite-dimensional weight subspaces if c is not an element of Z/2. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Orthosymplectic Lie superalgebra Supersymmetric differential operator Oscillator representation Irreducible module Polynomial algebra Exponential-polynomial function
DOI	10.1016/j.jpaa.2020.106530
收录类别	SCI
语种	英语
资助项目	NSFC[11671381] ; NSFC[11321101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000573401500007
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52270
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Xiaoping
作者单位	1.Chinese Acad Sci, Inst Math, HLM, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xiaoping. Conformal oscillator representations of orthosymplectic Lie superalgebras[J]. JOURNAL OF PURE AND APPLIED ALGEBRA,2021,225(3):24.
APA	Xu, Xiaoping.(2021).Conformal oscillator representations of orthosymplectic Lie superalgebras.JOURNAL OF PURE AND APPLIED ALGEBRA,225(3),24.
MLA	Xu, Xiaoping."Conformal oscillator representations of orthosymplectic Lie superalgebras".JOURNAL OF PURE AND APPLIED ALGEBRA 225.3(2021):24.