  The Heun operator has been cast, in terms of the elements of an underlying
$su(1,1)$ algebra, under specific parametric conditions, for the purpose of
spectrum generation. These elements are differential operators of
\emph{degrees} $\pm 1/2$ and $0$. It is found that the regular singularities at
$0$ and $\infty$ of the general Heun equation must be \emph{elementary} under
the required parametric conditions. The spectrum generation has been
demonstrated through a set of examples.
