Singular Conformal Oscillator Representations of Orthosymplectic Lie Superalgebras  

作　　者：Xiao Ping XU 

机构地区：[1]HLM,Institute of Mathematics,Academy of Mathematics&System Sciences Chinese Academy of Sciences,Beijing 100190,P.R.China [2]School of Mathematics,University of Chinese Academy of Sciences,Beijing 100049,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第12期2131-2149,共19页数学学报（英文版）

基　　金：Supported by National Key R&D Program of China(Grant No.2020YFA0712600)。

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 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 lλ2-λ1,where l is any positive integer and it is not a generalized Verma module.

关 键 词：Orthosymplectic Lie superalgebra supersymmetric differential operator oscillator representation irreducible module polynomial algebra SINGULAR 

分 类 号：O152.5[理学—数学]