An explicit geometric description of certain components of Springer fibers for
S
L
(
n
,
C
)
SL(n,C)
s given in this article. These components are associated to closed
S
(
G
L
(
p
)
×
G
L
(
q
)
)
S(GL(p)\times GL(q))
-orbits in the flag variety. The geometric results are used to compute the associated cycles of the discrete series representations of
S
U
(
p
,
q
)
SU(p,q)
. A discussion of an alternative, and more general, computation of associated cycles is given in the appendix.