Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new ind...Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.展开更多
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 orthosy...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.展开更多
文摘Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.
基金The project supported by National Key Basic Research Program of China under Grant No. 2004CB31800, 2006CB805905 and National Natural Science Foundation of China under Grant Nos. 10231050 and 10375087 Ding thanks Prof. A. Bellen for his warm invitation and great help while Ding was staying in Trieste, where the work was partially complected. Thanks also to Prof. G. Lindi for his kindness. And the work is （partially） supported by Inistero degli Affari Esteri-Direzione Gen- erale per la Promozione la Cooperazione Culturale, and by Istituto Nazionale di Alta Matematica, francesco sev- eri （INdAM）, Roma.
基金Supported by National Key R&D Program of China(Grant No.2020YFA0712600)。
文摘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.
