  The minimal representations of Sp(r,R) can be realized on a Hilbert space of
holomorphic functions. This is the analogue of the Brylinski-Kostant model. It
can also be realized on a Hilbert space of L^2 functions on R^r. This is the
Schr\"oodinger model. We will describe the two realizations and a
transformation which maps one model to the other. It involves the classical
Bargmann transform and can be seen as its analogue.
