Conformal oscillator representations of orthosymplectic Lie superalgebras
Xu, Xiaoping1,2
AbstractIn 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.
KeywordOrthosymplectic Lie superalgebra Supersymmetric differential operator Oscillator representation Irreducible module Polynomial algebra Exponential-polynomial function
Indexed BySCI
Funding ProjectNSFC[11671381] ; NSFC[11321101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000573401500007
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Document Type期刊论文
Corresponding AuthorXu, Xiaoping
Affiliation1.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
Recommended Citation
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.
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