  Let G be a unimodular Lie group, X a compact manifold with boundary, and M
the total space of a principal bundle G--> M-->X so that M is also a strongly
pseudoconvex complex manifold. In this work, we show that if there exists a
point p in bM such that T_p(G) is contained in the complex tangent space of bM
at p, then the Bergman space of M is large. Natural examples include the gauged
G-complexifications of Heinzner, Huckleberry, and Kutzschebauch.
