  The conformal transformations with respect to the metric defining the
orthogonal Lie algebra o(n) give rise to a one-parameter (c) family of
inhomogeneous first-order differential operator representations of the
orthogonal Lie algebra o(n+2). Letting these operators act on the space of
exponential-polynomial functions that depend on a parametric vector a, we prove
that the space forms an irreducible o(n+2)-module for any constant c if the
vector a is not on a certain hypersurface. By partially swapping differential
operators and multiplication operators, we obtain more general differential
operator representations of o(n+2) on the polynomial algebra C in n variables.
Moreover, we prove that the algebra C forms an infinite-dimensional irreducible
weight o(n+2)-module with finite-dimensional weight subspaces if the constant c
is not a half integer.
