  The n-dimensional projective group gives rise to a one-parameter family of
inhomogeneous first-order differential operator representations of sl(n+1). By
partially swapping differential operators and multiplication operators, we
obtain more general differential operator representations of sl(n+1). Letting
these differential operators act on the corresponding polynomial algebra and
the space of exponential-polynomial functions, we construct new multi-parameter
families of explicit infinite-dimensional irreducible representations for
s(n+1) and sp(2m+2) when n=2m+1. Our results can be viewed as extensions of
Howe's oscillator construction of infinite-dimensional multiplicity-free
irreducible representations for sl(n).
