Let
K
K
be a compact connected semi-simple Lie group, let
G
=
K
C
G = K_{\mathbf C}
, and let
G
=
K
A
N
G = KAN
be an Iwasawa decomposition. To a given
K
K
-invariant Kaehler structure
ω
\omega
on
G
/
N
G/N
, there corresponds a pre-quantum line bundle
L
{\mathbf L}
on
G
/
N
G/N
. Following a suggestion of A.S. Schwarz, in a joint paper with V. Guillemin, we studied its holomorphic sections
O
(
L
)
{\mathcal O}({\mathbf L})
as a
K
K
-representation space. We defined a
K
K
-invariant
L
2
L^2
-structure on
O
(
L
)
{\mathcal O}({\mathbf L})
, and let
H
ω
⊂
O
(
L
)
H_\omega \subset {\mathcal O}({\mathbf L})
denote the space of square-integrable holomorphic sections. Then
H
ω
H_\omega
is a unitary
K
K
-representation space, but not all unitary irreducible
K
K
-representations occur as subrepresentations of
H
ω
H_\omega
. This paper serves as a continuation of that work, by generalizing the space considered. Let
B
B
be a Borel subgroup containing
N
N
, with commutator subgroup
(
B
,
B
)
=
N
(B,B)=N
. Instead of working with
G
/
N
=
G
/
(
B
,
B
)
G/N = G/(B,B)
, we consider
G
/
(
P
,
P
)
G/(P,P)
, for all parabolic subgroups
P
P
containing
B
B
. We carry out a similar construction, and recover in
H
ω
H_\omega
the unitary irreducible
K
K
-representations previously missing. As a result, we use these holomorphic sections to construct a model for
K
K
: a unitary
K
K
-representation in which every irreducible
K
K
-representation occurs with multiplicity one.