Let M be a Harish-Chandra
module associated to a finite length, admissible representation of real reductive Lie
group G0. Suppose that p is a parabolic subalgebra of the complexified Lie algebra of
G0 and let n ⊂ p be the nil radical of p. In this paper, motivated by some
recent work in the study of zeta functions on locally symmetric spaces, we
make a comparison between homological properties of M and homological
properties of the minimal globalization of M. In particular, if p has a real
Levi factor, we are able to show that, after conjugating by an element from
G0, then the n-homology groups of the minimal globalization of M are,
in a natural way, the minimal globalizations of the n-homology groups of
M.
