  Random matrix models of disordered bosons consist of matrices in the Lie
algebra g=sp_n(R). Assuming dynamical stability, their eigenvalues are required
to be purely imaginary. Here a method is proposed for constructing ensembles
(E,P) of G-invariant sets E of such matrices with probability measures P. These
arise as moment map direct images from phase spaces X which play an important
role in complex geometry and representation theory. In the toy-model case of
n=1, where X is the complex bidisk and P is the direct image of the uniform
measure, an explicit description of the spectral measure is given.
