Let Z=G/H be the homogeneous space of a real reductive group and a
unimodular real spherical subgroup, and consider the regular representation of
G on L2(Z). It is shown that all representations of the discrete series,
that is, the irreducible subrepresentations of L2(Z), have infinitesimal
characters which are real and belong to a lattice. Moreover, let K be a
maximal compact subgroup of G. Then each irreducible representation of K
occurs in a finite set of such discrete series representations only. Similar
results are obtained for the twisted discrete series, that is, the discrete
components of the space of square integrable sections of a line bundle, given
by a unitary character on an abelian extension of H.Comment: To appear in GAF