典型文献
Singular Conformal Oscillator Representationsof Orthosymplectic Lie Superalgebras
文献摘要：
In our earlier paper, we generalize the one-parameter (c) family of inhomogeneous first-order diff erential operator representations of the orthogonal Lie algebras arising from conformal trans-formations to those of orthosymplectic Lie superalgebras, and determine the irreducible condition. This paper deals with the cases when the irreducible condition fails. We prove that if n?m?1＞ 0 and c is an integer satisfying 1≤c≤n?m?1, the representation of osp(2n+2|2m) has a composition series of length 2, and when n?m?1 ≥ 0 and c ∈ ?N, the representation of osp(2n+2|2m) has a composition series of length 3, where N is the set of nonnegative integers. Moreover, we show that if c∈(max{n?m, 0}?1/2?N)∪(?N), the representation of osp(2n+3|2m) has a composition series of length 2. In particular, we obtain an explicit presentation of the irreducible module with highest weight (e)λ 2?λ 1, where (e) is any positive integer and it is not a generalized Verma module.
文献关键词：
中图分类号：
作者姓名：
Xiao Ping XU
作者机构：
HLM, Institute of Mathematics, Academy of Mathematics & System SciencesChinese Academy of Sciences, Beijing 100190, P. R. China,School of Mathematics, University of Chinese Academy of Sciences, Beijing 100049, P. R. China
文献出处：
引用格式：
[1]Xiao Ping XU-.Singular Conformal Oscillator Representationsof Orthosymplectic Lie Superalgebras)[J].数学学报（英文版）,2022(12):2131-2149
A类：
Representationsof,Orthosymplectic,Superalgebras,erential,orthosymplectic,superalgebras,osp,2n+3
B类：
Singular,Conformal,Oscillator,Lie,In,our,earlier,paper,one,parameter,family,inhomogeneous,first,order,diff,operator,representations,orthogonal,arising,from,conformal,trans,formations,those,determine,irreducible,condition,This,deals,cases,when,fails,We,prove,that,satisfying,2n+2,2m,has,composition,series,length,where,set,nonnegative,integers,Moreover,show,max,particular,obtain,explicit,module,highest,weight,any,positive,not,generalized,Verma
AB值：
0.463175
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