Abstract In 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 → ∈ C n , we prove that the space forms an irreducible o s p ( n + 2 | 2 m ) -module for any c ∈ C if a → is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general supersymetric differential operator representations of o s p ( n + 2 | 2 m ) on the polynomial algebra C in n + m supersymetric variables. Moreover, we prove that C forms an infinite-dimensional irreducible weight o s p ( n + 2 | 2 m ) -module with finite-dimensional weight subspaces if c ∉ Z / 2 .

中文翻译：

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正辛李超代数的共形振荡器表示

摘要 在本文中，我们将共形变换产生的正交李代数的单参数（c）族非齐次一阶微分算子表示推广到正辛李超代数的表示，并确定了不可约条件。让这些超对称微分算子作用于依赖于参数向量 a → ∈ C n 的超对称指数多项式函数的空间，我们证明该空间形成了任何 c ∈ 的不可约 osp ( n + 2 | 2 m ) -模C 如果 a → 不在某个超曲面上。通过部分交换微分算子和乘法算子，我们在 n + m 超对称变量中的多项式代数 C 上获得了 osp ( n + 2 | 2 m ) 的更一般的超对称微分算子表示。而且，