LAUSR

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 .