  An iterative procedure for the explicit construction of the nontrivial
subspace of all symmetry-adapted configurations with non-zero weight in the
ground-state of the infinite-dimensional Hubbard model is developed on the
basis of a symmetrized representation of the transition operators on a sequence
of Bethe-Lattices of finite depth. The relation ship between these operators
and the well known mapping of the infinite-dimensional Hubbard model onto an
effective impurity problem coupled to a (self-consistent) bath on
non-interacting electrons is given. As an application we calculate the
properties of various Hubbard stars and give estimates for the half-filled
Hubbard model with up to 0.1% accuracy.
