  We discuss the representation theory of $H_f$, which is a deformation of the
symplectic oscillator algebra $sp(2n) \ltimes h_n$, where $h_n$ is the
((2n+1)-dimensional) Heisenberg algebra. We first look at a more general setup,
involving an algebra with a triangular decomposition. Assuming the PBW theorem,
and one other hypothesis, we show that the BGG category $\mathcal{O}$ is
abelian, finite length, and self-dual.
  We decompose $\mathcal{O}$ as a direct sum of blocks $\calo(\la)$, and show
that each block is a highest weight category.
  In the second part, we focus on the case $H_f$ for $n=1$, where we prove all
these assumptions, as well as the PBW theorem.
