Singular Conformal Oscillator Representations of Orthosymplectic Lie Superalgebras

作     者：Xiao Ping XU Xiao Ping XU

作者机构：HLMInstitute of MathematicsAcademy of Mathematics&System Sciences Chinese Academy of SciencesBeijing 100190P.R.China School of MathematicsUniversity of Chinese Academy of SciencesBeijing 100049P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第12期

页      面：2131-2149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 Key R&D Program of China(Grant No.2020YFA0712600) 

主　　题：Orthosymplectic Lie superalgebra supersymmetric differential operator oscillator representation irreducible module polynomial algebra singular 

摘      要：In our earlier paper,we generalize the one-parameter(c)family of inhomogeneous firstorder differential operator representations of the orthogonal Lie algebras arising from conformal transformations to those of orthosymplectic Lie super algebras,and determine the irreducible *** paper deals with the cases when the irreducible condition *** prove that if n-m-10 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 ***,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 *** particular,we obtain an explicit presentation of the irreducible module with highest weight lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.